The "pre-occupied with something else in particular" seems clear in all dictionaries I have checked. "Can't focus on work because I am in love and cannot stop thinking about my boyfriend." Usage does seem to vary though (can't focus on *anything* due to, say, depression)
Two dictionaries also give 仕事 specifically as examples. 

sankoku: 手に付かない（句）ほかのことに気を取られて、そのことに心が集中しない。手がつかない。「仕事がー・仕事も手につかず」
nikk:　他に心が奪われて、その事に身がはいらない。落ち着いて物事の処置ができない。手がつかない。
daijs: 心が他に奪われてその事に集中できない。「うれしくて仕事が―◦ない」

 n-grams give other work-related items I encountered.

Common work-related collocations:
手につかない	60565
仕事が手につかない	13679
勉強が手につかない　3254
家事が手につかない	288
何も手につかない　3254　(often with ほど or くらい, but too large for n-grams. nothing can hold my attention = unable to concentrate on anything)

Hard to find a positive collocation. Really seems to be primarily "cannot focus on responsibility because distracted by love/fun (or sometimes depression)". 


Did an image search for the phrase, and followed some article links...

What to do when you can't focus on anything because you are too in love with your boyfriend...
カレのことが好きすぎて何も手につかないときの対処法4つ 
https://googirl.jp/renai/200608001/
カラダやココロが重くて、何も手につかない焦り
やるべきことはあるのに、何も手につかない焦り
失恋や告白で、気になってしまって何も手につかない

What to do when you can't focus on anything...  (because you're exhausted from work, depressed, too focused on your love live, ...)
何も手に付かない状態から脱するためのアドバイス！
https://grevari.com/article.php?id=834
仕事で疲れていたり…
疲れてないけど焦っていたり…
落ち込んでしまったり…
恋愛のことが気になりすぎてしまったり…

Worried so you can't focus...
「気になって手につかない」ときの３つの解決策
http://kikukoto.net/2019/07/02/hft/
Could be coincidence, but he only uses "手につかない" when for "thinking about someone you're in love with, can't study".  Other expressions are used with negative preoccupations.(mistake at work, 集中できない, family troubles, 何も頭に入ってこない)
「好きな人のことが気になって勉強が手につかない」
「仕事の大ミスが頭から離れず目の前のことに集中できない」
「家庭の問題が解決せず何も頭に入ってこない」

ALL returned inflections of 手につく
Negative forms:
手につかない	60565
手につきません	21995
手につかず	17727
手につかなかった	7799
手につかなくて	2902
手につかないで	480
手につかぬ	442
手につけない	322
手につかなかったら	64
手につかなければ	55
手につきませんで	34
手につけません	33

Positive forms
手について	24165
手についた	17906
手につく	6800
手につける	3753
手についたら	971
手につきます	579
手につきました	163
手につきまして	167
手につけます	87
手につけば	47

All n-gram particle prefixes:
手につかない	60565
が手につかない	22443
は手につかない	940
で手につかない	196
に手につかない	222
と手につかない	225
の手につかない	50

Not generally used as an adjective:
Top 10 N-grams Lookup for 手につかない (Frequency Order)
手につかない	60565	  
手につかない状態	4417	  
手につかないの	2045	  
手につかない・	1988	  
手につかない・・	1888	  
手につかないん	1697	  
手につかないほど	1587	  
手につかないし	1572	  
手につかないよう	1569	  
手につかないくらい	1555	  
手につかないよ	1554	  

==== vs 手がつかない
daijs:
デジタル大辞泉「手が付かない」の解説
手てが付つか◦ない
「手に付かない」に同じ。


手につかない	60565	65.4%
手に付かない	17965	19.4%
手がつかない	11249	12.2%
手が付かない	2770	3.0%

This entry is an example of something I would like to work on improving in general, if there is an appetite for it in this group.  This falls into a class of entries where the J->E gloss is perfectly serviceable when used with a specific context, but hard to make sense of in the J->E direction.  A particular issue is lack of cues to grammatical relationships between subjects and objects when they don't align with the English gloss.  

===

With regard to the previous edit, I think the "on" was important...  This phrase generally takes a grammatical subject with が which equates to the object in the English expression. Xが手につかない　= "cannot focus on X(due to being preoccupied with something else)". I've replaced "distractions" with "preoccupation" for specificity. It appears, for example, that this would not be the first choice for "I'm unable to work because there is noisy construction outside". 

I've removed [adj-i] as a note for discussion, and added [vi].  This is not, generally, used as an adjective. It is the "dictionary form" of a negated verb. So, you can expect all the usual negated forms （ません、ず、ぬ、なかった...).  n-gram counts for 手につく inflections included in the references.  Yes, this entry's surface form is structurally an い　adj, but it would be far more useful for a computer to know that this entry is identifying the negative inflection of a specific verb... Is there a way to indicate that?  (note: this seems somewhat related to github comments on the entry 虫も殺さぬ).

One other shortcoming of [adj-i] is that it's particularly unclear that a grammatical subject figures into the expression. Tagging as a "intransitive verb" at least makes that possibility a little more apparent.

Only with regards to the [adj-i] bit, there is something similar with the 手に負えない entry.  This gets a corresponding 手に負える entry with [see=手に負えない], and a comment [note="usu. in the negative"]. Not sure if 手に付く warrants that kind of entry though, but it would allow people searching on inflected forms to make their way back here... I'm not advocating for that entry, just thinking about possibilities.

==
Because why not do 7 crazy things at once... I've added 手が付かない as an [sK] form to this entry. nikk says there is a subtle variation between the forms, but daijs and sankoku both list as absolute synonyms, so I am imagining the distinction was lost over time. Looking at the simplest かない inflection, が is 15% of overall usage, which is more than enough to actually display it as a surface form.  But if it's displayed, it will garble up the readings with [restr=] tags.  If it's possible to avoid a duplicate entry for 手が付かない, that seems preferable to me, but maybe 仕方がない... please let me know and I can propose a separate entry in the usual way, and maybe xref it back here.

... The more I think about it, the more I think　が needs its own entry. But in any case I will at least wait till this entry is resolved, then we can duplicate the final entry (if desired).

==
big general note: I am neither a native Japanese speaker, nor an expert on Japanese.  While I try very hard to understand issues before commenting, please don't take these comments as authoritative or as a claim to greater knowledge than anyone in this group.

@@ -13,0 +14,8 @@
+<k_ele>
+<keb>手がつかない</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
+<k_ele>
+<keb>手が付かない</keb>
+<ke_inf>&sK;</ke_inf>
+</k_ele>
@@ -19 +27 @@
-<pos>&adj-i;</pos>
+<pos>&vi;</pos>
@@ -21 +29,2 @@
-<gloss>unable to concentrate (due to distractions, etc.)</gloss>
+<gloss>unable to concentrate (on something, esp. work, study, etc.) (esp. since preoccupied with something else)</gloss>
+<gloss g_type="lit">(something) fails to hold one's attention</gloss>

I think it can be even briefer. The meaning is clear.

@@ -21 +21 @@
-<gloss>unable to concentrate on (something; due to distractions, etc.)</gloss>
+<gloss>unable to concentrate (due to distractions, etc.)</gloss>

trailing "on" followed by (due to distractions) looks kind of weird, is this better?

@@ -21 +21 @@
-<gloss>unable to concentrate on (due to distractions, etc.)</gloss>
+<gloss>unable to concentrate on (something; due to distractions, etc.)</gloss>

着 is not in the kokugos so I'm assuming it's iK.

@@ -11,0 +12 @@
+<ke_inf>&iK;</ke_inf>

G n-grams:

手につかない	60565
手に付かない	17965
手に着かない	2672

@@ -5 +5 @@
-<keb>手に付かない</keb>
+<keb>手につかない</keb>
@@ -8 +8 @@
-<keb>手につかない</keb>
+<keb>手に付かない</keb>

@@ -18 +18,3 @@
-<gloss>to not be able to concentrate on (due to distractions, etc.)</gloss>
+<pos>&adj-i;</pos>
+<misc>&id;</misc>
+<gloss>unable to concentrate on (due to distractions, etc.)</gloss>

Entry created