Currently sat working now on My Vista PC which did have some similar issues to the ones you have described.
Whe on the internet especialy whilst running downloads or sites with a lot of flash animation, videos etc it would lock up completely. Also copying or downloading large files did seem to be a problem as well.
I think I have it sorted now but did have to make a few changes.
1. Put in a brand new GraphicsCard. The motherboard came bundled with a PCI-e graphics card of its own brand which was Vista certified (acording to the box) but changing that for a ahlf descent ATI card seemed toget rid of the locking up whils on the net.
2. Copying / dowloading files (and sometimes just for no reason at all) PC seemed to stop responding with HDD light stuck on. Tried a few things and in the end it came down to a dodgy PSU. Fitted a new one and here I am surfing the net again.
I know these are not exactly the same issues as your customer but they may help.