A good battery does not put out 14.5 volts. The alternator will charge at 14.5 volts, but the battery should be around 12.5 volts.

I would check your battery cables for good connections. Sounds like when you put a load on it, you loose the connection. Remove, clean, and reinstall your battery cables at the battery. If that fails to work, follow the cables to their first connection point and verify those are clean and tight.

You should also charge the battery, then load test the battery. This will tell you if the battery is good.