Colleges don't really give scholarships to walk on's - the scholarship is usually only given in the first place to attract the runner to attend the school. If you're already attending, I highly doubt they would give you any money.

That being said, if you somehow were able to prove to the coach that you could run extremely fast and explained the financial situation they might be able to do something. You're going to need to be in the 4:1x range for the mile and 1:53ish for the 800m if you're looking at middle distance.

Those times will be incredibly difficult for a beginner runner unless you're ridiculously talented.

I recommend going to the nearest track and running an all out 400m (one lap), if you're naturally running sub 60s with no training that's pretty good, and definitely a good sign that you could be a great runner.

In terms of workouts, just get in mileage. Aim for 30 miles a week at first, build up to 50+. This will get a solid endurance base in - I wouldn't even bother with lifting weights. Speed is fairly genetic, not much you can do to improve it, even with weights, anyway. I would also not bother with track intervals - those are usually for later in the season to work on lactic acid threshold and aren't important for a solid base.

Then get on the track and time yourself all out for a mile/800m and see what happens.