Normally don't do it, but I download what was supposed to be a trial program called "Registry Cleaner". Every time I boot up this thing starts running. I have gone to the Install/Remove section of My Computer and tried to remove it. I get a window that says it is being removed, but then I always get a small window with the message "Invalid install log file". How can I get rid of this program?

To remove from start up..click on start>run>type msconfig click on start up tab..uncheck[untick]
Registry Cleaner..click apply>ok>reboot your system..
Check in files and folders..start>find>files and folders>find registry cleaner program and delete all referencies to that program..

Got rid of it. Thanks. Was this a problem with my computer or do these people make it so hard to delete that they hope you will just subscribe to it?

No pc is no doubt ok? many referencies to d/loaded programs always hang around..
You will find more entries in the Registry but only go there if you understand how the Registry works
and know what you are doing and always back up the Registry before making any changes.