Won't power on, vibrates every 5 seconds, with replacement battery.

So my battery has seen better days, won't last a whole day (with very sparing use, I'm not a phone junkie) and sometimes dies at like 35%.

I figured it was time for a new one. Ordered the best reviewed kit on amazon.

The replacement process goes fine, and I get the phone all buttoned up and plug it into a charger... and it just sits there with a black screen, vibrating like it's recognizing a power cable every five seconds.

Now from what I've seen online, this has to do with a damaged display, or at least damage to the connection between the motherboard and the display.

So I check the connection, nothing is damaged or kinked, but I disconnect and reconnect the cables and try again. Same symptom. I then reconnect my old battery (failing, but at least with some charge and known to work) and the phone boots right up.

Is this a bad replacement battery? A battery that just needs to charge for a while to get up to a useful load? Something else wrong with the phone?