My very rough guess is that any repair charge would probably be 30% or more of the cost of a new GX1, and you'd still end up with a quite-used (possibly abused ;)) GF1 that may be reaching the end of its lifespan. I upgraded from a GF1 to a GX1 and it is a substantial improvement. I'd say put the money into a new camera body that will work better and longer.
Or compare the cost of repair to buying a used GF1. There's a way to check the shutter actuations on a GF1, and you could perhaps get one that is much less used than yours for about the cost of the repair.
I'd still upgrade to a GX1, though, if it were my decision.