It sure does sound like a dead battery, here are a few things you might try. With, a volt meter checked the power supply that connects to the Roomba. Using your volt meter put the positive lead from the volt meter inside the barrow of the power supply and the negative lead to the outer barrow you should measure a constant 22 volts D.C. If you have the docking station use the volt meter to test the output of the docking station by putting the leads from the voltage meter across the two metal contacts on the base station it should measure about 4 volts D.C. If both reading are correct, you might try just charging the Roomba directly using the power supply and not using the base station. I?ve once had a docking station that would measure the correct voltage however it still would not charge the battery correct even though the voltage was correct it would discharge the battery.
But if the battery has sat a long time and the voltage has dropped too far down in the battery, the battery might not take a charge. So to answer your question your battery might be too discharged to take a charge at all.
Sorry about you problem give those idea a try and see if they make any difference.
Way too many of these guys running around, I need a new hobby.