You could try this. Plug your computer in and press and hold the power button for 10-15 seconds. If it is stuck in sleep mode this may force it to shutdown. Now hopefully it will start up again the next time you press the power button. To prevent things like this from happening, I always turn the hibernation and power saver functions off. Good Luck
ADDED
Looks like your cat found the shortcut to put your computer to sleep :-) First check again to make sure that none of your keys are stuck.
Then try this as well
1) Press and hold the power button for 8 seconds.
2) Turn your computer on.
3) If the computer says says “Windows was not shut down successfully” etc., just select “Start Windows Normally” and press the “Enter” key.
If you still do not get any results, remove your battery,your AC power supply and your memory.
You are saying that you had disconnect the battery as well as the AC power supply at the same time. This did not make any difference. It did not get you anywhere but stuck at the flashing light with a black screen? Try an external monitor and make sure it is not anything with your LCD. Also make sure that you have disconnect any other devices like mouse, flash drive, anything at all,disconnect it. When you restart your computer, hold the F2 Key, it should let you boot into the BIOS and go from there. If none of this works, last try would be to clear the CMOS. I have the Service Manual on my file server and do feel free to download it. It will help you further with the trouble shooting as well show you how to reset your CMOS. Good Luck to you and I hope that this helps a bit. Let us know how you are progressing. I don't think it's the cats' fault.....;-)
One More Addition
try this as well, shut down the computer, take out the power cord, take out the battery. Press and hold down the power button for 2 minutes. Put the battery back in, and then the power cord, and now turn on the computer.