I know the CMOS batter is flat - could this be all that the problem is ?
I wouldn't think so. Normally the manufacturers create the POST (Power On Self Test) per:
1. Do some very crude motherboard tests/initialisation (eg. CPU, first 16K memory, support chips), then
2. Initialise display, then
3. Do remainder of POST.
During step 1, the display isn't active and so the main way the POST indicates any problems is via beeps from the speaker.
Beeps can also be heard during step 2 if the display initialisation fails.
And so if you hear beeps, it's a basic problem. A low/dead CMOS battery sounds like a basic problem, however from my experience, it's not something that would stop the computer going past step 2. Normally a low/dead battery results in error messages on the screen.
However, the battery could be the problem. It comes down to the engineering. For example, designers of the Trio CS-2110 oscilloscope failed to include an isolation diode for the settings battery (backed up the front-panel settings), which results in a low/dead settings battery causing the CS-2110 not to work.
What does two beeps mean? There is no standard. Different manufacturers use different beep patterns, and manufacturers have also changed the meaning of the beep patterns between models. I couldn't find anything on the Internet. The T3100E user/technical manual possibly has the answer.
I don't think the 'leaking battery' scenario that chuckcmagee suggested as a possibility is probable in this case because the T3100E uses a Lithium battery. I've only ever seen the NiCad ones leak. But it's possible.
If you know the battery is dead, maybe you should buy a replacement, open up the machine, replace the battery, and while you're in the machine:
1. Do a visual inspection.
2. Reseat any chips that are in sockets. Moving them up by about 2 milimeters is enough, then push them back down. Use static protection procedures.
3. Reseat any connectors.