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If your database is intact, all you should need to do is upload your XOOPS files, then you need a mainfile.php with all the correct info for your site and database. If you don't have a backup of mainfile.php, you could rebuild it, by looking for a file called mainfile.dist.php. Then look through it and fill in all the things with your info.
You will need to define:
for your site
XOOPS_ROOT_PATH
XOOPS_URL
for your database
XOOPS_DB_PREFIX - you can get this from your database
XOOPS_DB_HOST
XOOPS_DB_USER
XOOPS_DB_PASS
XOOPS_DB_NAME
Once they are all defined, rename that file mainfile.php, if all your info is correct you should be all set.
Depending on what version of XOOPS you had and what version you are going to use, you may need to upgrade the Xoops, instuctions are usually in an upgrade folder.
I think that will get you going.
--Edited--
I forgot about the modules, you will need to add the modules you were using to your module folder.
You could find which modules and which versions they were in your database, in the modules table.
Once you get it back, make a backup of all your files.
John