the fork light you speak of is a hydraulic function disabled light, it tells you the forks will not operate when the battery light is on, and if i'm not mistaken if all conditions are not met when mounting the lift, the conditions being, seat switch engaged, seat belt buckled, truck in neutral before you drive, and maybe even the parking brake set, that sort of thing. If one of those functions are not working correctly then the truck will not initialize and enable the lift/drive circuit and that light will come on.
At least on most newer forklifts thats the way they work now and has actually been this way for several years now.

if the battery light is off now then that part has been corrected, you may want to check the other things i mentioned. And be prepared to call a toyota tech to come out if you can't figure it out ;o)

good luck