Yes, the system device manager says I have "USB 2 enhanced host controller". I have 2 USB ports on the front of the machine that I believe are USB 2. I have a USB MIDI controller that works in either of those but doesn't work in any of the USBs at the back, suggesting they are the "enhanced" ones.
Would I be right in thinking that by plugging an M-Audio Fast Track Ultra into one of these I could record 4 tracks with condenser mics plus another 4 at instrument level simultaneously? If so, that seems to be exactly what I'm looking for.