iPhone won't power up and battery won't charge after replacing

I've read through all of the battery-related questions I could find, and I think that I may have just received a defective battery, but I thought I would throw this one out anyway since I didn't see anything that exactly matches my situation.

I bought the iFixit replacement battery kit, and the replacement went according to plan. I tried powering on the iPhone to test it, but I got the empty battery gauge with the thin red line and the icons underneath it showing a plug pointing to a lightning bolt.

I then plugged it into the wall charger, but I never hear the happy "I'm charging" chirp. Both charger and cable are Apple and work fine with my other iOS devices. The icon below the battery gauge changes to a lightning bolt only, so I know it's detecting the charging cable.

Since I get the screen with the empty battery gauge even if unplugged, I'm assuming that the power contacts on the battery are connecting properly.

I've left it on the charger for several hours, and it never moves off of the thin red line, and I don't feel the back of the iPhone get warm.

I went ahead and disassembled the phone again. Reassembled it, checking all the cables and connectors, making sure the contacts for the battery were clean, and made sure all the cables were seated firmly. Everything looks fine, but I still just get the empty battery gauge. I can't replace the old battery, because it's all puffed up, and I don't really want to risk the possibility of it catching fire or anything.

For what it's worth, I put a multimeter to the battery contacts. If Pin 1 is closest to the dock connector, here is what I got when I connected the following pin pairs:

1-2: 0 ohms

1-3: 2.4V

1-4: 4.09V

These figures are consistent with the values reported in an answer that I read here. I'll leave conclusions to those with greater knowledge of the workings of the battery packs.

Is it possible that it's a simple case of having received a defective replacement battery pack?