Nikon D3300 Battery Questions

Yesterday I took out my D3300. I hadn't looked at it for some time. The battery was dead so I charged it. It must have been charging for about 90 minutes. The charger did not indicate that the battery was fully charged but the camera powered up and the battery icon indicated a full charge. I then took out a new battery which had been sitting for maybe a year or two unused. I put it in the charger but no light on the charger came on. Is it just a bad battery or should I have kept the old battery in the charger until a full charge was indicated?

I may have answered my own question. I put the new battery in the camera and it shows as fully charged. I didn't think it would hold the initial charge for so long.

See how it goes; you may be lucky. What the true capacity of this battery is, you'll only be able to find out by using it. Don't be surprised if it runs down very quickly; it may appear to be full, but that doesn't mean its capacity is on spec. In general, LiIon batteries don't like being stored entirely full. It's best to discharge them to around 50% for long-term storage.
Anyway, just use it and see how it goes. If it works, then great. If it doesn't, you know why and just get a replacement.

No personal knowledge of the D3300 but on the D90 you can check battery health in the battery menu.