There are two possible causes for this problem that can be fixed on your own. I have experienced both (not in the order presented below :-) ).
Most likely cause in general is battery exhausted and not recharging due to insufficient power supply voltage. Most micro-USB chargers are rated for 1.0A current; the Asus T100 requires 2.0A.
Due to Li-Ion battery design, when it is just "topping off", the Asus will require less than 1A of current. Therefore, practically any charger will be able to top off the Asus.
But when it is markedly discharged, the Asus will attempt to suck the full 2A of current, and this will drop the input voltage a bit. If the power supply is not the original one, and is only rated for 1.0A, the voltage drop will be enough to drive the voltage outside the battery controller's "comfort zone", and the red LED light will power on (since current is being drawn) -- but the battery won't recharge, as the controller won't allow it. With some aftermarket chargers you will notice the light on the charger going off, then on, then off, continuously.
PC USB ports also sometimes have an overcurrent protection, so that they won't charge a flat-batteried Asus even if they will allow it to top off.
Solution is of course to use the original Asus power supply, or a power supply with a higher current rating, typically 2.1A (be careful; higher current ratings will not damage the Asus, but higher voltage ratings, rare as they are, definitely will). You want to have exactly 5.0V (the USB standard) and equal or more than 2.0A. Standard smartphone chargers are 1.0A or less, and will definitely not work, even if they might work when the Asus isn't completely flat. Some tablet chargers are 2.1A and will work.
The other possibility is a faulty battery connection. The battery has an internal connector covered by a transparent yellow adhesive protection film, but there are reports that the connector might sometimes not be plugged all the way in. Unless you're very very careful, this will void the warranty: insert a guitar pick or a thin hard plastic sliver between the bottom of the tablet and the screen. Drive it gently all around, and you will see the catches snap open. The cover must be slid out towards the USB power plug; do not force it open there, or you might damage the USB connector. Once removed the shell, you will see the battery (a double silvered flat package) and four connectors. The battery one is covered by an adhesive film. Try picking loose the adhesive film; the connector shouldn't move. You can use a hard plastic sliver to pry it loose and re-seat it until it clicks, then replace the adhesive film. When putting back the cover, first slide it over the USB connectors; don't simply press it in place. After the connectors are slotted in the back cover, then you can press the cover in place (you can just snap each catch closed by pinching screen and cover together with thumb and forefinger in corrispondence of each catch).
I have an ASUS WD11 tablet running Win8 and experienced a similar issue. I can't remember if the solution was to try another charger all together or to use my phone's USB to AC charger, which is why I'm posting as a comment. My charger was showing signs of life too, illuminating the red charging light. Still, it wasn't until I tried using one of the two mentioned chargers that my ASUS tablet would accept and retain a charge to boot. – root – 2013-12-19T13:43:41.530
You likely can't without sending it to ASUS. You can try another charger or if the tablet offers a user replaceable battery a new battery. – Ramhound – 2013-12-19T19:16:34.553
If it's into warranty, have it RMA'd – arielnmz – 2014-06-04T17:12:15.517