just a suggestion first of all, and I'm not getting at you. Try and leave a space on each part. It helps to space it all out to read
Well, CD copying, etc uses alot of resources since its always looking at the source, and back to the disk again, and since you have onboard sound, this is why you are experienceing choppy sound.
ONBOARD SOUND:
You see, onboard sound uses the processor to run music, and if there isn't enough power left, it'll work on the CD instead, since this is to the PC, the most important thing you are doing, and so, skips to not stop the copying process and cause an error.
The best thing first of all would be to get a cheap dedicated sound card to plug into a spare PCI port. These can be very cheap (a Creative one would be best) and would free up resources.
COPYING PACKAGE:
Nero is the best CD/DVD copying package though, and so you shouldn't be getting slow downs. Have you tried copying with no sound running? And no programs running in the background?
Plus, what speed is your actual copier? You may find your sisters is a faster drive.
When in Nero, its best to check settings. You see, if you are copying MP3's for example and want to run them on another device, its best to choose Finalise as an option, but if you are running on the computer only, taking this off will speed things up slightly (not by much),
Plus, check that Simulation is not running, and that it is burning straight away (another option you can select from settings just before copying). Simulation basically doens't burn, and just tests if everything would work correctly.
COPYING MUSIC:
I'd use Windows Media Player 10 to do this if I were you. It can rip MP3 files and WMA files, and is alot faster you'll find (Check the bitrate it is ripping at. Higher bitrates will give better quality sound, but will take up more space, as well as it taking a longer time) (128-192kbps is standard for alot of uses)
I hope some of these suggestions help
EXTRA NOTES:
As for installing games, DVD drives tend to be a bit slower at this if its a DVD disk (speeds in DVD haven't got as fast as CD), but to speed up the process since you have onboard sound, turning off music would help ALOT.
Like I said, getting a dedicated sound card should help speeds quite a bit if you are experiencing choppyness
Even a Sound Blaster Live card (About 10-15quid) would be better than what you have now. (Offers 4 channels)