Question
 

I just realized that my Sony computer came with the DVD burner. Do you think they are reliable for backing up PS2 DVD games? If so, what software can I use with Sony computers? Because I tried installing Roxio and it gave me problems.

It's Good..the Problem is your PS2..The odds are your PC is eqipped with DVD+R drive and not DVD-R Drive..
DVD+R is not that good with PS2's in general but decently good from Ver.5 and up machines about .90% or more compatible because there are some games out there you can burn but it won't work with DVD+R's where DVD-R will work..
As for Software, Roxio sucks..Try nero..