The most common and most likely answer to this crossword clue is the 10 letter word CHILBLAINS
I've seen this crossword clue in The Guardian
C
H
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Buddy explains!

The straight part
We know that "Digital problem" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case digital problem = chilblains.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CHILBLAINS mean?
CHILBLAINS noun- An itchy purple red inflammation of the skin, especially of the hands, feet and ears, occurring when capillaries below the skin are damaged by exposure to cold weather.