First, the pro-forma: Better to uninstall the application rather than just delete the files. Yes, it doesn't help, but it is true and someone will bring it up, so saving time...
Now, assuming that you just want the SID to be able to go through. Normally, the SID is stored in the registry HKEY_LOCAL_MACHINE\SOFTWARE\Oracle. It can be in several places there. Please note that several pieces of Oracle software use this key (e.g. Oracle client) so be careful; probably worth backing up with a registry export command first.
You would also need to check the Windows Services (from a command prompt, type "services.msc"). The Oracle services begin with "Oracle" in their name, so they are easy to find. If you see some with the SID in the name, you probably need to remove them before installing. I would use SC.exe to install this as explained here (http://stackoverflow.com/questions/330836/how-to-uninstall-a-windows-service-when-there-is-no-executable-for-it-left-on-th).
If you want a more complete purge, you are in for tons of registry editing, as Oracle often leaves other stuff in the registry.
Good luck, and I hope that this helps,