i recently have been getting a similar problem, see new recently backed up games i have have black scrolling lines on them, and then a little later the didnt work at all. I checked the methods i used, like using DVD Decrypter on the same media, at the same speed. They just dont work, but my old backups worked. I do have a new pc but this shouldnt be the problem.
Convert PAL to NTSC or NTSC to PAL------>http://forums.afterdawn.com/thread_view.cfm/167922
ScubaPete's guides------>http://www.dvdplusvideo.com/tutorial007.html
Bbmayo's guides------>http://home.comcast.net/~bbmayo/index.html
My ever-growing movie collection------>http://www.intervocative.com/dvdcollection.aspx/squizzle
scratch that...you said you tried to copy an old backup you already had to no avail....hmm im stumped...let us know if you get it straightened out dude
you havent tryed a voodoo ritual.some evil spirit is preventing you from making a working backup.every possible solution has been tried.i was gonna say upgrade your modchip bios but you tried a game that worked before and it didnt work now.then it might be your decrypter settings but you also used Nero.whatever curse you have dont give it to us(just kiddin).
it looks like a long process of elmination.you could start by cleaning and possibly adjusting your ps2 lens closer to the disc(counterclockwise).eliminate simple things that wont involve making unnecessary backups.then work your way towards other possible causes.
it would have helped if you had swap magic.one good benefit to swap magic is you can test your backups on someone elses ps2 to see if the problem lies with the backup or the ps2.so you would have a better sense of how to fix the problem.you said the games play some of the time.that would mean the games copied to the disc.the speed wouldnt be a factor as far as it not being able to boot.it seems it is having trouble reading the files to boot the game.
are you using DVD+R or DVD-R?dvd-r are suppose to play better on older ps2 like yours.if you had the other computer you could have tried to use that to see if it has something to do with it.since that is a known computer that has worked for you.just throwing some ideas at you.if any of that stuff works you can call me the exorcist.if not,then getting a real exorcist might be an option.