This phrase functions as the subject of the sentence. Here's why:
* Gerunds are verb forms ending in "-ing" that act as nouns.
* Subject is the person or thing that performs the action of the verb.
In this case, the gerund phrase "Crying about your problems" is the thing that performs the action of the verb "will not solve". It's the subject of the sentence, just like "He" would be the subject in a sentence like "He will not solve them."