If a yota has trouble sarting all the time, it is unusual. We had an 85 4runner 15 feet down a mine shaft, spent 5 hours in the middle of the night (yes alcohol was involved) winching it out. That bad boy started up first try. 2 roll overs and a 98 and 95 started right up. It is not a jeep. Dont get me wrong i love jeeps, but...well...its a jeep thing. thats why i drive a toyota.
If the truck was running i think your alternator would be putting out plenty enough to actuate that solonoid.
I second the tranny fluid check. Did you change the oil in the tranny to something different or new?