I don't have a solution, however I do have an HP G4010 working fine in Slackware 13.37.
What I find curious is the light not coming on, and you get an image. I would have guessed you would either get nothing, or a black image.
FWIW, on my 64 bit system, I have x-sane 0.998 and sane version 1.0.22 installed. My light comes on as soon as I turn the flatbed on with the power switch. Sane does not turn it off, so I have to make sure I power the flatbed off after use.
I'm using the genesys backend. From lsusb;
Bus 001 Device 005: ID 03f0:4505 Hewlett-Packard ScanJet G4010
Debain is slow at making newer versions available, at least that is what I have read. Any chance you have older levels of sane?