2009 Toyota Corolla No Start - Need Help!

#1
My girlfriend has a 2009 Toyota Corolla. We thought its battery had gone bad so we put a new one in it, it is the correct battery. After parking it for 2 days with the new battery it dies again. Can't unlock with the key fob, no lights inside turn on at all, no lights when turning the key, no crank/start. Is this for sure a bad alternator? The car never died while driving it ever.

2 months ago the key got stuck in the ingition and had to be wiggled out, took like 3 minutes both times. Could this issue be caused by an ignition switch? If it was an ignition switch how would that explain no lights turning on? Also, the gauge cluster light has not been working in 2 months, can't find a blown fuse or anything. Would a bad alternator explain this too?

If you need any extra information please leave a comment! I need help though! Thank you
 
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