Replace the tent.

Normally I would say putting $120 into an MSR product would be worth it compared to $150 for a generic product, but tents have lifespans. If the rain fly is sticky, the floor is not far behind. Rain seeping through your ceiling is bad... next to that is having water seep up through your floor. The two functions of a tent are to stay dry and keep the bugs out. Your MSR tent most likely (even with a new fly) will fail at the first and being 20 years old probably has more than a couple holes that make it less effective against the second.