As a reminder, here's what happened yesterday.
 
After trying to resuscitate it with some cold air and cleaning today, I eventually I gave up and ordered a 250GB Slim. Costs a bit more than repairing it but I'll get it much sooner and I'd much rather have a new system with new warranty than a repaired one that could go again at any minute. Of course, there was still the issue of the game being stuck inside, but with the use of some screwdrivers I managed to open it up and make my way through the tricky disc tray to get it out. Also removed the HDD, so if that still works I should be able to transfer my save data to the new 250GB HDD.