Think of it like your video recorder... The tapes are read and recorded by a "head" in the VCR yes?
A CD/DVD player is the same. Back in the old days, and until relatively recently CDRW/DVDRW drives had a number of different heads. This was nessecary as reading a cd or dvd is not the same as writing a dvd, and so it needed a different laser and write method to do the job (a far far finer laser).
The drive probably has a seperate DVD write head which has burned itself out. It's quite common, especially on heavily used or older drives. It will still read DVD's because the read head is working perfectly well.
That said, with no more information it's early days to be saying that as an absolute certainty, however likely it may be.
First, open device manager, uninstall both the primary and secondary IDE controllers, let it reboot, and it should re-detect and reinstall your devices. Try again and see what happens. Don't be put off by the terminology either - it's just what their called, and the way they're listed.
The second thing to try is a firmware update.
If it deoesn't work after that, It's probably the dvd write head burned out, and it may not be worth the hassle for the price of a new one (£30-40 in the UK)