At this point, I'm pretty sure this thing is screwed up beyond any repair.

This was a hand-me-down from my sister. She had used it for probably 3-5 years before giving it to me.

In the middle of my last exam, my TI-84+SE crashed, booted up, then wouldn't respond to button input (besides ON to turn it on, where it would just display the blinking cursor and nothing else.)

Returned to it after a few months to try to repair it before school started so I wouldn't have to buy another.
Using TI-Connect a bit to try a couple back-ups fixed it, but not for long.

After I had received the false hope that this thing was fixed, I installed zStart, and promptly made it so this appears:
as well as messing with a few settings.
This was great and all until I transferred zhelplit.8xp, basically a hotkey readme file.
I ran it on my calc, and used 2nd + Quit to close it.

and...

It crashed. Guess what happened next.

Yup.

No button inputs were registered, except for ON, of course.
No problem, I'll just restore from backup.
That didn't work, so I asked some people on SAX for help.
"Use ON + DEL/CLEAR"
Nope
"Use the reset button"
No reset button on the TI-84+ apparently
"Take out the batteries for a bit and press each key one by one"
Nope
"Check for stuck keys"
None
"Use TiLP to dump a rom and see if it's a HW or SW issue"
I did, and the rom worked on jsTIfied just fine.
So it must be a HW issue.

I took out the back-up battery, and it was pretty corroded.
Luckily I had a replacement, so I put both aside while I checked the circuit board for any further corrosion or something.
Everything looked fine there.

Replaced the Back-up Battery and it's still the same.

Is there any hope, by chance?

My calculator was on 2.53MP when I installed zStart before I upgraded it to 2.55MP when re-installing the OS, if that helps.

Corroded batteries always screw things up, even if you can't see the damage. There may be one more thing you can try though. Clean out the I/O port (the headphone jack looking thing). I've heard cases of calcs acting strangly because something got stuck in the port.

There's probably more you can do, but that's all I know.

TLM 888th post!

Didn't check the I/O port, but apparently just leaving it alone for a couple of days fixed it for a minute or so before freezing and going right back to how it was.

At this point, I'm probably going to just get a new one. ¯\_(ツ)_/¯

Thanks for all the help!

Huh. This sounds very odd.

Have you tried the special key commands here?. From what I read it seems you have done a few, but not all. I recently had a problem with my 83+ not turning on, like the screen did not, but the calc did. This was caused by corrupted RAM (who knew). I would try some of these commands. I would also strongly reccommend running the TIOS Self-Test. I know it is not registering input at the moment, but if you get it working, try [Mode] + [Alpha] + [S]. This checks the hardware.

Good luck.