Lights are staying on just alittle bit on Dodge Ram 1500 2002

We had the engine rebuilt. Then it sat for some time.my
husband was ill. I would go and try to start it every week
but it would always be dead. Then one time I was there at
dark and saw that the lights were on just a little bit. So I
charged it then left the battery disconnected. It’s been
over a year my husband is some what better. We got a
new battery and then as he was driving home it drained
the battery so we got an alternator. The lights are still on
alittle bit an the alternator isn’t charging. Help what’s
going on please