So you plug your Transformer into its power adapter, and the charging indicator stubbornly refuses to come on.
Remember you assembled your power adapter from two parts? Disassemble it again. See those two flimsy bent-wire pins that are on the body of the adapter and which should mate with your country-specific plug?
Sometimes they just don't. Very, very gently bend those two pins outward - just a little - and then reassemble the power adapter.
Your Transformer should charge again now.
Didn't work, huh?
Try putting your charger in a plastic bag and popping it into the freezer for a while.
No, really. The freezer.
Apparently there's a thermal cut out which doesn't sometime play well with the fact that the charger can get hot.
This post was brought to you by "OH NO! WHAT DO I DO? MY TABLET WON'T CHARGE," several cups of coffee and a small heart attack.