Mine has 168K currently, it was a mechanics special. I posted on here about it if you want to read. In short, these are incredibly vehicles, especially if the wife and/or kids are going to be in it. Very safe too. The 2UZ is a 400K mile engine (at least) with proper maintenance.
I thought you were looking at one on the lot, but it sounds like you are able to take it home. Even better. I thought the 99s had a security system on it. For mine, it's just below the screen/button and above the radio, all by it's lonesome. I know the 99s don't have this layout with the touchscreen, so I am not sure. I would expect a red light though.
My first thought is that the starter could be on it's way out intermittently. The starters on these are under the plenum, not on the side like I6 cruisers. To replace it, you have to remove it, there are some links in the FAQ on how to do it. Probably a 3 hour job for the first time as I have read. Even if it isn't the starter, it would be a good idea to replace/rebuild it as the date/miles are getting up there. I went ahead and had my mechanic replace my with a new denso unit while he was RnR the #2 head, it wasn't that much more since he was in there.
Outside of that, I would check if it's getting fuel. Perhaps the filter is clogged? I have changed them on various cruisers before but almost all the time they are good. More PM I suppose.
Is it throwing a CEL at all? Since these have coil packs, a P0300-P0308 would be thrown if one were bad. Or, pull a couple of them and check the spark plugs? Could be another culprit.
Not sure if that helps or not. I don't think any of the above items would be expensive, just take time to figure out. If you have any other questions on it in general, feel free to PM/email me.