There may be some hints of what's happening in the Windows event viewer, look at the application log for messages from SilverFast or possibly the system log.
Try removing any non-essential USB devices except for the scanner and your keyboard/rodent, and connect the scanner directly, not through any external USB hubs.
It looks like Silverfast supports win 7/64 bit, so you should be ok there.
One possibility is that the Epson Scan component that reacts to the scanner's scan button is keeping Silverfast from accessing the scanner. But, silverfast should be able to handle that.
Another, perhaps more likely cause is that Silverfast didn't install properly. The easiest way to deal with that would be to uninstall and re-install.
Then, to install it again, try right-clicking on the Silverfast installer and selecting "run as administrator". If the installer auto-launches when you insert the CD, exit from the installer, then browse the CD in explorer to select it.
You may want to temporarily disable any anti-virus software. It would also be a good idea to try the install after freshly booting the machine.