SM-T210R Stuck in boot loop; Download mode available, but not Recovery.

Alright, so I had my Samsung Galaxy Tab 3 7.0 (SM-T210R) rooted and had a custom recovery and ROM flashed. (TWRP and RocketTab respectively.) Nothing was wrong, everything worked fine, and then the battery died. I didn't plug it up immediately because I didn't really have a need to, but when I did this afternoon, it was stuck in a boot loop, infinitely repeating the Samsung Galaxy Tab 3 splash screen. So I tried to go into recovery mode and back it up, but I couldn't. Recovery mode would not open, even during the boot loop while charging. (I think it was charging anyway.) I can get it to go into download mode fine, but it will not go into recovery mode no matter what I do. Before starting trying pretty much anything I could find that looked reputable, download mode said:

ODIN MODE
PRODUCT NAME: SM-T210R
CURRENT BINARY: Custom
SYSTEM STATUS: Custom
HW REV: 0x5

After trying to flash the stock rom and recovery, it says:

ODIN MODE
PRODUCT NAME: SM-T210R
CURRENT BINARY: Samsung Official
SYSTEM STATUS: Custom
HW REV: 0x5

And I am still unable to get into recovery, and it is still stuck in the boot loop any time I plug it up. I should also mention, that no button combinations or even just the power button do ANYTHING when the tablet is off, but I know the battery is ok because if I plug it up, get it into download mode, and then unplug it it's fine. It's just during the boot loop.
I'm honestly just lost. Can anyone please help?