Hi Robert,
I'm going on the assumption that the phone booted and was working before replacing the battery; is that correct?
If so, you'll want to go back in and double-check your work. Disconnect the battery and use a magnifying glass and bright light to examine both sides of the connector; that on the motherboard and on the battery flex cable. Look for any bent or broken pins; bent ones can frequently be straightened with fine tip tweezers.
Once you're satisfied, clean both sides with 90% or higher concentration isopropyl alcohol, then reassemble and test.
If it still isn't working, I'd suggest taking out the replacement battery and reinstalling the original; it's always possible the replacement you got is defective so if the old one works that would tend to confirm it. If you don't have the old one any longer, it might be worth considering just buying another battery from a different supplier given they're pretty inexpensive these days.
Do you get any indication of the battery's charge? If the dock connector isn't working then it wouldn't be able to charge the battery so if wouldn't be able to boot if the replacement battery doesn't have any charge in it, so you might consider replacing it if the old battery or a different battery doesn't work.
Give some or all of those ideas a try and let us know what you find.