1) Try leaving it plugged into the charger (not the computer) for 24 hours. IF the battery is almost completely dead, the first couple of hours puts about enough charge innto the battery that it might be able to turn the tablet off, but not much more.
2) If you've regularly been using the battery until it's down to around 10% or less, 2 years is a long life. It may be time for a new battery. (Deeply discharging a lithium ion battery gives you between 100 and 250 charge cycles.) The longest life, and considering that it's not cheap or easy to replace the battery in a tablet, that's what you want, is recharging when the battery gets down around 40% to 60% of charge. (Yeah, I know, you want the longest time between charges. But that's not how lithium ion batteries work, they're the most power-dense batteries we have, you can't change the laws of physics and chemistry, so you're stuck between long charge times or long battery life - you can't get both.)