I left it overnight in case it was still doing something, but it was just as dead this morning.
I did a battery pull and when I re-inserted the battery the phone came back on (without pressing power button) to a white screen with a spinning hourglass and a small icon top-right. That lasted for a couple of minutes and then a progress bar saying "Patching OS" appeared. This took about 3-4 minutes to move up to 100%, and then it started again at 0%. This time it got up to 34% and then the phone turned off again (with a brief red flash from the LED).
Now it's in the same state as last night, powered off and no buttons will do anything. Tried another battery pull and the LED then goes red for a couple of seconds when I re-insert the battery, but otherwise it's still dead and won't power up.
Help! Any advice?