yes, upgradind the firmware could solve the problem.. but not likely.
here is a list of firmwares for various brands :
http://www.burnworld.com/firmware.htm
but i dont understand why the dvdrom dont read the disk?
if im not mistaken the trail had to be downloaded (an image file) then burned on a cd. maybe your burn process failed? my trial worked fine but now that i bought the original, i dont wont to download and burn a new trial disk.
Try burning the cd again or check if the cd works on any other drives (if you dont have one yourself, go see a friend and check it out there).
There shouldnt be any problems installing it. Since every cd out there are compatible with older and newer drives since the manufacturers knows that upgrading the firmware isnt for the average user. you can even make your drive go FUBAR, which isnt good.
If you **** up during a firmware upgrade and the drive stops working you can just throw it in the bin.
Are you sure you a 64bit CPU? you didnt say that in the specs. Since windows xp 64x wont install on normal 32bit cpu's.