[Zeke]

Soldering on a mini circuit board is tricky because originally it was all done at once. If you can place the button on the spot where it was and it makes contact, you could use a thick version of Super Glue (cyanoacrylate glue) to hold it. I buy mine from Mohawk but if you look around you might find some at a hardware store or hobby shop.

After looking around a bit I see that Gorilla and Loctite have some cyanoacrylate gel on the rack maybe even at the home box store. Use a toothpick to apply and don't let it flow over to the contact points.