Bad battery. You could try taking it to a Mac Store, an authorized repair store, or using the iFixit guide try and replace it yourself. One last step to try would be a DFU restore. NOTE; it will wipe everything off the device.
@C00lb0y1231 Please perform a DFU reboot. I would also think about trying the old "device in rice" trick to pull anymore water out of the device. Shut off the the device, and put the device in a container of rice overnight. Of course you could get some dry bags which pull all moisture out. Once this is complete, please hook the device into your computer and launch iTunes. Ignore all the messages for now. Turn the Device on holding the home button and power button for 10 seconds. Count this out as it has to be 10 seconds or it will boot back into recovery. After 10 seconds release the Power button BUT DO NOT RELEASE the home button. Continue holding the home button until iTunes registers the device. Note; the device screen will remain black so do not be alarmed. Restore the device.
I'm willing to bet the internal battery is shot, as is in mine. I'm sure you have swapped the main batteries 4 AAA's if I remember correctly. If you look directly above those you will see a little screw and should be able to replace the internal battery. I don't have the exact version, as I have a TI84 Plus, but I remember the battery compartment being very similar. Update: It could be than that the logic board final went kaput. :( I know my buddies went out in a similar fashion. His started having screen graphic issues, than would die soon after replacing the batteries. Have you tried calling Texas instruments to see if maybe they have any other possibilities? Sorry that unless I have the device, and take a look at some of the terminals, I can't think of any possibilities.
If your device can get into recovery mode than you should be able to boot into DFU mode. Just to reiterate proper DFU instructions: (1) Plug Device into Computer and Open iTunes. (2) Turn Device off completely. (3) Hold Power and Home for 10 seconds (Display will turn off, hold for ~2 more seconds after this) (4) Release Power and continue holding until the device registers in iTunes. If the device registers in iTunes it is DFU and should be able to be fully restored. I realize you state you could not get into DFU, I am just asking to try once more and report back. Update: @Con I have fixed it with a DFU restore before. I usually had that error when the IPSW wasn't being signed anymore by apple. I had to download the latest IPSW from a third party site, one that didn't have my SHSH blobs attached to the IPSW before it would work. Although that was an error -1 if I remember correctly. Good call on the hardware failure. Look at the other topics posted, it sounds like water damage or possible hardware failure...
P C Were they correctly installed by you, or installed factory? I have had experience in the past that if they are incorrectly installed they may have damaged the RAM slot itself rendering the slot faulty or even broken all together. You could also try a PRAM reset (Option+CMD+P+R at boot up, let cycle three times) and an SMC reset as well after having both correctly installed.