Check if working in US before taking to Europe + getting Greek SIM car

I have an unlocked Nokia 3310 I bought about 8 years ago and used several summers in Greece. The SIM card has obviously expired, and wouldn't work here in US anyway. When I plug the phone into a power source, it beeps but no screen display ever comes on. How can I tell if it still works? Or if the battery should be changed? (I last used it about 5 years ago).

Could the problem be that I taped the cover so is not fully closed? I did that because it is so hard to open the case. If I close it all the way, I'm afraid I will never be able to open it again.