losing Power...Electrical

The other night My car died. I got it jumped and got it home barely...it was choking and would barely run. It also backfired through the intake. Today I changed the Battery and it fired right up and ran smooth. Now its losing power again. Lights are dim and it sounds like its going to start running bad again. I have a new alt. and a new Battery, is there anything else I should check? I'm getting the Alt checked tomorrow. Thanks in advance.
Kevin.
I posted this on maxima.org, but I thought I'd let you guys have a crack at it.

Alternator is bad, problem sovled

get urself a multimeter and check it urself
hehe

look up...I figured it out.