We're about to turn on our furnace, but we have a problem.

The thermostat is broken! Now, this problem is easy to identify. The thing takes two AAA batteries, and ONE of the four battery connectors is slightly askew. Instead of bending out to hold the battery in and complete a circuit, it bends in a little. It therefore doesn't touch the battery, no circuit is completed, and the thermostat doesn't work.

We can replace it for $20, but I really would rather fix it if possible. It seems like it ought to be a simple fix to pull the connector out and have it bend properly again! Any ideas?