I just got a Ti-84 from a friend and it had corroded terminals so i had to clean those out first.

When I did, it turned on and everything worked, but I realized I hadn't put in the backup battery so I put that in while the calculator on and after that it stopped taking input.
It'll turn on and the blinking cursor is in the top left, but when i try to type something, nothing comes out.

I've tried resetting the ram, new batteries, cleaning the terminals again, nothing's worked. Is there anything else I can do?

Welcome to Cemetech, Isa108. It sounds likely that the battery corrosion damaged the mainboard, and is specifically making it appear to the calculator that a key is always being held down. Just to make sure, try pressing and releasing every key on the keyboard (one after the other, not all at once) and see what happens. Do you have the tools to take it apart to check if there's any physical damage from corrosion to the mainboard?

Something weird just happened, I took out the batteries for about 30 minutes, put them back in, (except the backup) and it worked for a good 10 minutes then I repeated the process and it's currently working (I don't have the backup in, I'm not too sure if this is necessary). is it more of a main board issue or an OS issue?

This may be a bit late, but try testing the keypad. On the home screen, press [Mode] [Alpha] [S]. Press [On] until the screen says 11. The number on the display represents the row and column on the keypad, so 23 would be [Del]. Just press each button until it ends.

Also check the link and USB port for anything stuck inside.