Personal Loan 13 yrs old, never repaid, can I sue?

Anybody can sue for anything, but your case appears weak.  The question is when was repayment due?  If it was due to be repaid 10 years ago, your case woudl be pretty weak (the statute of limitations for breach of contract, which generally runs from the date of the breach, would have passed) but still not hopeless because (a) sometimes statutes of limitations can be extended if, for example, the other person acknowledged their indebtedness to you since the limitations period ran, or if they somehow concealed the fact that they hadn't paid, etc.