Problem with switches on a toy circuit board
The fact that both switches are misbehaving in the same way suggests that something that is in common has failed, rather than one of the switches or connections to it.

Unfortunately, it's not obvious what that would be. (The worst case is that it is actually the controller IC under the blob.)

I think you will have to figure out what the circuit is intended to be by following all the traces (e.g. the switches probably have one side in common but does it lead to Vcc or GND?) and making a schematic, then probing around with a voltmeter (or an oscilloscope if you have one) to see where the real signals disagree with what should be there given the schematic.