Archive and install your OS if you can. Don't do a clean install unless you need to. However, if you do this I would customize the installation to remove eveything you don't need from it to help slim the OS down. You can load them on later anyway, so why even install them now if they'll just eat hard drive space up. Just my opinion. However, I would install X11 and Rosetta just in case yoou have legacy applications that need it. These are actually useful, but drivers for printers aren't. Some apps actually need to use X11, too. This is why I say keep it.
Are your discs retail or the grey disc?
Put the disc in the drive and press C or hold the Option key down. Select Mac OS X Install DVD. Let it load to the installer and then install it. The install should explain itself.
Put Disc #1 and repeat the first step and press C or Option to boot into it. Let it take it's sweet time. Install from the first disc(don't alter this one; it has the iLife suite and other apps the computer came with. The retail doesn't.)
After this, when it says insert Disc #2, put the 2nd DVD in the drive. This should finish the install. Hopefully this fixes the issue. If it doesn't the Bluetooth board is shot. Replace it internally or get a Mac friendly dongle. Look for a Broadcom based one.
This part is for the Antiglare machine. It will not work in the glossy computer. As such, I assume it's part of the panel if yours is the glossy version. I assume you can, though.
MacBook Pro 15" Unibody (Mid 2009) Bluetooth Board