How to attach Oracle database backup files to existing server

The above files are not enough. The above are datafiles, but not all of the datafiles you need to start the database. Most importantly, you are missing the SYSTEM tablespace's datafile(s). Have your client do the following queries:

SELECT name FROM v$controlfile;
SELECT member FROM v$logfile;
SELECT file_name FROM dba_data_files;

The client should shut down their database and then copy all files returned from the three queries above. In addition, they should also send you the parameter file. You'll need all of these to get the database up and running.