Sometimes, *sometimes*, on the old PS2, if you eject the disc and then reinsert it, it will re-read and might go through. Mine has had problems focussing (I seem to have to adjust the focus up or down a notch manually every time I load between racing and menus. It will often flick to the red icon, and after a few seconds I just eject the disc and reinsert it. Sometimes it can take a few goes, but it will eventually read.
You could try adjusting the focus of the laser (or getting the PS2 serviced). That may be the problem.