Presumably, when you've managed to stop it using Task Manager, Lr still shows the same behaviour in not starting? To ask the obvious, did you install any new programs, install updates to Windows etc or alter your computer just before Lr starting mis-behaving?
At the moment, if you did do any installs etc, the best bet I can suggest might be to use System Restore to roll back.
What are you seeing?? You say nothing appears on screen yet you talk of trying to Optimise???
Do you get any messages??
Also have a look in the catalog folder to see if there is a file in there ending in .lock, if so delete it.
Thanks for the input.
Turns out Lightroom not guilty. The hard drive containing the catalogue was failing and although tests seemed to show it as OK it was actually only reading / writing at a fraction of the correct speed. So Lightroom was taking a long time to read it's own catalogue. It tooks 48 hours to copy 1 gig of data off the disk.
Happy you found the solution before the drive was dead...