They said "the problem is with the C: partition, not the actual disk drives".
They've sent me another diagnostics tool to run, so I'll do that once I can get everyone out of here and see what it says.
First sign of trouble was when I rebooted last week. I got a message saying "One of your disks needs to be checked for consistency" and it suggested I run Chkdsk. In stage 2, the following message appeared over and over again on screen: "Correcting error in index $I30 for file 206436". Had to power off and start again, this time bypassing Chkdsk.
I'm seeing two NTFS errors in the Event logs now:
"The file system structure on the disk is corrupt and unusable. Please run the chckdsk utiility on the volume\Device\HarddiskVolume2"
"The file system structure on the disk is corrupt and unusable. Please run the chckdsk utiility on the volume C:"