Going to the Toshiba page, and doing a search for the specs for L577 computers, I see a variety of models, with different suffixes, and different price points. But even the model with the lowest price has enough memory (4 GB) and a strong enough processor (AMD quad core) for windows. So I'm inclined to say, "yes", you should have no problem running any of your Trainz versions, or the other software you mention.
The biggest concern for Trainz 09 might be (note, I wrote "might be", not "will be") the display. If that turns out to be the case, one way to deal with that issue might be to switch from full screen mode, to running in a window. That worked for me with TS 12, for a while (although while you got a whole new laptop, I only got an upgraded graphics card).
With respect to the other items you mentioned, Sketchup, and Paint.net, I expect both would run, but that there might be a limitation on the size of object you could create, or image you might edit. I doubt that these should be a concern, though, because any object too big to create in Sketchup, or any image in Paint that cannot be edited because of memory limitations will be too big for Trainz, anyway.
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. its a Toshiba windows 7 satellite L577 with 425gb and i don't know how much ram though. and i want to know if it can run my trainz 09, paint.net, and goggle sketchup 8 i wanna know if ill be able to run these programs without any problems and stuff.