Where Can I Buy A Replacement Battery?

Hello,

I own a Apple iPad 1st Generation 64GB 3G/GPS or A1337 of which when I plug in and attempt to turn on boot-loops. When I attempt to put it into DFU mode and plug it into a PC or Mac it will either immediately turn off (the iPad only boot-loops when plugged in) or if I used a adapter that allowed it to be plugged into power and the Mac or PC at the same time, it would not show up on iTunes. I'm 95% sure that it is a battery problem meaning I need a replacement battery. I looked on the iFixIt Store and the oldest iPad they supply parts for (let alone battery replacements) is the iPad 2 and anywhere else I could find that supplied battery replacements for the iPad 1st gen were on sketchy websites or hosted by sketchy sellers on places like EBay and AliExpress (even Wish at one point)

If anyone can help by sending a link or showing me a place to find a replacement battery I would be really grateful.

Thank you,

-Jenson