A read-only filesystem does not necessarily mean that you need to reinstall the operating system. Usually, it is caused by filesystem corruption. Your data center can take the server offline and run an fsck (FileSystem ChecK) to repair the filesystem so that it can be mounted read-write. If the corruption is very severe, you may need to reinstall the operating system, but that is not always the case.
You really need to talk to your data center about running an fsck before committing to completely reinstalling the operating system.
It is really not practical to completely reinstall the operating system (by first formatting the hard drive) without losing data. Since the filesystem is probably corrupt (which is why it is mounted read-only), trying to back up data now has a very real chance of backing up corrupt data that will not restore correctly. This is where the backups you made before the problem happened become useful.