Re-installing Oracle does not erases your datafiles. However you should backup them before.
If you have only one disk with all the data it should be something like this:

c:\oracle
c:\oracle\ora81 --> This is the RDBMS directory, this will be replaced in installation...

c:\oracle\admin --> This is where your init, udump, bdump, etc, shoud be. This will NOT be erased.
c:\oracle\oradata --> The DataFiles. This will Not Be Erased.

But if i understood you correctly you have another server with an healthy Oracle RDBMS.

If that is the case then replicate the file structure that you have on the original server, and follow the steps on the previous post. Create service using Oradim...and so on...

Hope this helps