This happened to a local ladyfriend of mine and was a nasty con to get into her comp..... She realised afterwards that no-one could know if her comp had picked up malware unless they already had access..................   but she gave access to her computer..... fortunately the penny dropped and she got a good friend of hers who is 'in the know' to safeguard her info... but it cost around £130 to do it........... thus possibly saving her bank account details and all transactions through e-bay etc been 'played with' to someone elses benefit.
So:-
Ask yourself the obvious questions such as who could this be and how would they know my comp is not working correctly... and "Should I let someone have access to my computer remotely?"