Prerequisite: You need to obtain evidence to prove that you bought a computer. An important piece of evidence is the invoice. Check to see if your name is written on the customer invoice. If your name is written, it can directly prove that you bought the computer. On the other hand, if your name isn't written on the invoice, or it's not written at all, you're still in trouble. As for the money you got from your mother and friends, it's hard to prove you used it to buy the computer. Of course, the receipt in your hand is a good thing after all, it can indirectly prove the money you spent to buy the computer.
Now that your girlfriend has run away and you don’t know her whereabouts, it is certainly impossible to file a civil lawsuit. The only option is to report the crime and recover the computer through criminal means. Of course, this is also difficult. The police will file a case, but it is not yet known when the case will be solved after it is filed.
Her mother won’t tell you her address, and there’s nothing you can do about her. If you want to report a crime, you should go to the police station where the computer was stolen, which is where you live together.
Hope it helps.