I finally managed to get the software to work after LSI said that the problem must be my fault. I had to manually trawl through my disk removing anything that SilverFast had installed, then reinstall SilverFast 8. So it looks like their upgrade process hadn't worked.
On a side note, I had an horrific customer experience over this, and I said as much to the customer support representative - who just ignored my complaint. At no point did they offer a refund or even apologise.
I will be actively looking for an alternative scanning solution in the future, this is the last LSI product I pay for.