Especially the official Korg website did not support T serious anyway. (It's weird M1 is still in the support list.) You can find the default program and combination voice Sysex file on internet. You have to learn this way after replacing you internal battery because all default voice will disappeared.
1. Make sure you have a USB-MIDI cable connected T3 to your computer. If not, you have to get one and have the cable driver installed.
2. Go to this webpage to download Sysex file.
You can download 1 to 4 and to load it one by one. (the reason will be described later)
Or you can download 5th to load it one time.
3. Download a Sysex player
You can use your DAW (Cakewalk, Cubase...) for it.
Or SysEx Librarian http://www.snoize.com/SysExLibrarian/ for Mac user
MIDI-OX http://www.midiox.com/ for Windows user
(remember to select MIDI Out to your USB MIDI cable)
4. Set your T3 ready for receiving Sysex data (It's important!)
Go to Global Page 1, set MIDI overflow to "ON", and EXCL to "O"
Go to Global Page 6, set Program Memory Protect to "OFF" and Combination Memory Protect to "OFF".
You will see the data receiving message during the data transition.
After that, all default Program/Combination voices will be loaded.
The reason why we would load 4 different Sysex files not the 5th or 6th in one time is the memory size not big enough both T3 or MIDI-OX. If there is error message on T3, just try it again or turn off/on T3 to see if all voices are back.
Hope you enjoy for the old guy - T3. Even it's born about 25 years.