I have a TI-81 that stop working, I installed the

It is possible that the screen dimmed too much after you changed batteries. One of the two procedures will work.

Press the [2nd] key and release it.
Press the UpArrow and keep it held down for a while. As you hold pressure on UpArrow key the screen should darken. Stop when satisfied.

Alternative.

Press [2nd] key and hold pressure.
Press the UpArrow repeatedly until screen darkens to your liking.

4 AAA batteries and one CR1616 or CR1620 button batter for backup

Source: http://en.wikipedia.org/wiki/TI-83_series

Having gone over a month without a response to my query, I assume the suggested screen adjustment solved the problem.

The button cell backup battery keeps the memory electrically refreshed when the calculator is turned OFF. The necessary power for regular use is supplied by the 4 AAA batteries (main power). That nothing happened when you put in a fresh set of (expensive) lithium batteries may be due to the screen being too dim to see anything.

If the calculator displays RAM CLEARED each time it is turned on, it may be due to a depleted backup battery. The battery model number is CR1616 or CR1620. On my TI84PLUS the backup battery is of type 303 (Sony) or SR44SW (Maxell).

TI calculators have an annoying habit of dimming the screen when the batteries are changed so that it appears as if the calculator isn't turning on. Turn the calculator on (or at least press the ON key). Press and release the 2ND key. Press and hold the Up-arrow key for a few seconds and see whether the screen becomes legible.

TI calculators have an annoying habit of dimming the screen when the batteries are changed so that it appears as if the calculator isn't turning on at all. Turn the calculator on (or at least press the ON key). Press and release the 2ND key. Press and hold the Up-arrow key for a few seconds and see whether the screen becomes legible.

Yes, the back up battery must be replaced.

I had the same problem, I took all five batteries out and left it for about an hour and put them back in and it turned on stating that the RAm was clear and now it works fine.

An electronics store or Radio Shack should carry this. Take your old one with so that they can test it - it should be at least 3V. The battery type is CR1616 or CR1620

Try replacing both the AAA batteries and the back-up batteries. This should probably fix the problem.