Sounds like you have a configuration issue preventing proper BIOS translation of the drives. If it cannot resolve the drives priority it can lock everything up at the BIOS level and nothing loads at all. Otherwise there may be a poor/missing pin/cable connection or internal drive problem.
Make sure the BIOS has the "AUTO" options set for the Master/Slave slots on the IDE channel you are installing on. If the Slave slot is disabled or set to CD it may not be detecting properly. Scratch the second drive for a minute and just install the A04 on the cable by itself, setting the jumpers for Cable Select (CS). It is documented that the A04 works best when on the Secondary IDE in the Master cable position. While you are changing it's position on the cable, check the pins where the cable plugs in . It is very easy for one of these to get just slightly bent, and when you push the cable on it bends it all the way down. Run into this a lot--just happened a few weeks back with an HP CD-RW that would read fine, but burn nothing. You also might want to test it with a different cable--preferably an 80 pin (ATA100 grade or higher) for good measure if you have one. If the pins are ok and it does not work when by itself in CS (or Master only) mode, then you have likely got a faulty drive.
If it works right when on the channel by itself, THEN add the DVD-ROM to the second spot on the cable. It should work fine if you set the DVD-ROM as Slave, but may need to set it as Cable Select as well. Sometimes you have to take the reverse approach and set the A04 as Master (slave present) and set the Slaved drive as CS. 9/10 times the jumper configuration is the culprit (after the bent pin or bad cable issue).
CD/DVD drives don't really need a special driver for Windows (they are mostly managed by firmware, the "driver" is more like a command bridge to the firmware). Since most all of them use the same generic driver, if one drive works just fine, the other should as well unless it has something physically wrong with it. The exception of course is burning software that requires a descriptor file update (ie px engine for RNM) or ASPI layer update so it can issue the right commands to control it properly.
If it ain't broke don't try to fix it! But, hell if you can tweak that bastard just a little bit more....hehehe.