Engine will not turn off with key - Accesories (power windows, etc. Have power with key removed)

The question comes in two parts:
1. My engine will not turn off when the key is turned off. I replaced the ignition switch as I thought that would be the obvious choice but that didn't fix the problem. Help!
2. Also all of the instrument cluster lights (chk engine, brake, park, oil, etc.) Stay on when the key is removed. The only way that I can get them to go out (so my batt. Doesn't drain) is to disconnect the batt. Help!

I thought that the new ignition switch would fix my problem but it didn't. It appears that there was nothing wrong with my old one as I can disconnect the harness to the switch and nothing changes.

Thanks for your time.
Joe