Hi,
There is a chance that u can restore ur database but tell me that whether u have created a new database and tried to copy the files from the backup.
See I have done this procedure.But for me I have to install the same database from one machine to another machine.If the following procedure helps u than it is well and good:=The procedure assumes that the Oracle server version is the same as ur old database version.

Step 1: Create the necessary directories in ur machine to keep all ur datafiles,logfiles,controlfile as they were before.

Step 2 : Copy the init.ora file in ur machine.Edit the control_files parameter to reflect the new directory where ur controlfiles will be kept.

Step 3: Create a service with the same name as the earlier service in Windows NT through the following command
oradim80 -new SID -intpwd oracle -pfile=

Step 4: Startup the instance
svrmgrl> connect internal
svrmgrl> startup nomount pfile=

If ur instance starts successfully shutdown the instance and then

Step 5: Copy all the datafiles,controlfiles and logfiles in their respective directory as they were before.If u want to make any changes in their destination directory mount the database and make the changes.

Step 6: After everything is done.Startup the database.If ur have previously taken backup is consistent then Oracle will not perform recovery and ur database will be as consistent as before.

In case of any help further needed please be free to ask to me at [email protected]

Regards,
Rohit Nirkhe,Oracle DBA,OCP 8i