I've recently had this most annoying thing happen. But I might not be able to help too much, there are a few differences between your problem & mine.

For starters, I'm using XP rather than Vista. Also, my 'disk problem' message didn't appear straight away...rather anywhere between 50 - 90% download. I could download music without a problem, it was only large torrents (movies) that triggered the 'disk problem'.
I have 60 GB of free space left on my HDD.

I ended up changing the location of my download folder onto an external HDD. Problem solved (touch wood) for me

Before that, I defragged the HDD (it's done regulrly but did it again anyway), Did a disk cleanup, checked the HDD for errors (right clickon the HDD > properties > tools > error checking > check now.

Start off by defragging your HDD, that's fixed the problem for a few people. Otherwise, check out these threads for more advice & things to try. These threads refer to XP but hopefully things are the same (or similar) for Vista.
The "disk problem" problem
Disk Problem??
disk problem
Low Disk Space Message