This "disabled scan button" problem is an easy one to solve!
Just drag with the mouse in the little preview image to select the part you want to scan. As soon as you select a rectangle, the Scan button is ungreyed and operates normally - you can scan the image. (This Macintosh OS X behaviour is different from using the scanner on a Windows PC, where the Scan button defaults to scanning the whole of the scanner glass and is not greyed out).
After a lot of internet searching, I found the comment by Bob Drake about 60% of the way down the webpage Mac OS X 10.4.5 Update: Experiences where he says:
Feb. 22, 2006
Image Capture WILL do a scan on an Epson 4870 scanner after the pre-scan ONLY if you select the outline borders of the area of the image you want to scan. Then the "Scan" button is functional. Epson Scan used to "guess" the borders, which you could then adjust. With Image Capture you MUST specify the desired area. Unlike Epson Scan there is no choice to save as a PDF. Is there anyway around this other than by opening and faux-printing in another application? It was nice to be able to quickly scan a raft of documents as PDF files using Epson Scan, which auto-numbered scans, and then bind them into a binder using Acrobat.
I tried the same thing with my old Epson 1250, and sure enough it solved my problem.