It's pretty easy to get lost in the game, and I had a hard time finding keys, so I looked around and was able to find this old walkthrough:
http://web.archive.org/web/20080224161547/http://killingtime.home.mindspring.com/

Some maps would be preferable, but this helped me out.

Holy crap, THANK YOU. I'd been spending days searching for a walkthrough and it looked like all trace of them had vanished from the internet. By the way, the URL you provided works, but the link itself takes you to the non-archived version which is gone. I think it's a problem with how GOG auto-formats links... so to everyone else, don't click, but copy-paste that link.