does it try to turn over at all, during these 10 cranks or no? if it is cranking over, does it seem to be weak cranks, like the battery is barely putting out enoughpower to the starter?
In either case above , it is starter related- either it is going out all together, or when these starters get some age on them, they get cranky in cold weather, the plunger doesn't wanna come all the way out, or not at all the brushes don't make good contact with each other, lots of little things. the hardest part of the starter repair is getting it off in the first place. otherwise any take down manual on these is pretty good, and their is a good link on here somewhere to take the starter apart, and another good link to show you the new parts/brushes/stuff
you wanna get for a good rebuild. A few hours labor yourself for the rebuild, and about 50 bucks in parts. Otherwise a shop is going to charge you 200 to 250 for a new/rebuilt starter, including labor. And if yo uget a shopto do it, make sure you get a toyota OEM starter, or a Denso starter, any other starter won't be near as good.
My starter just went out on me, lasted 250k miles and 22 years though...