Jim,
This sounds like a possible damaged Woodruff key, which is sometimes referred to as a "shear key." As others have said, damaging this key will change the engine timing, which makes starting and running difficult or impossible.
(The main purpose of the key is to protect the drive shaft from getting bent if the blade hits a hard object. The key shears and prevents much of the sudden jolt to the blade from being transferred to the driveshaft. Hopefully. The same principal is used on boat engines to protect the engine if the blade hits an object under water.)
Obviously, the entire (free?) tune-up by the college kids was a mistake. I'd suggest going over the entire mower to determine what they fouled-up besides a loose blade and low oil.
Also, I'm confused by what you mean when you say that "the blade spins freely". Do you mean that you can turn it easily when you have the mower turned on its side?
(Don't forget to be careful to always tip the mower in the correct direction when observing the deck. You want the carburetor side of the mower to be up when the mower is tipped. Also, avoid using an impact wrench when removing or installing the blade. The impact wrench can damage the Woodruff key.)
If it is reasonable time-wise, you may want to get the college class to go over the mower again IF the instructor is aware of the problems and the half-assed job the students did. This is a learning opportunity for the students and worthwhile for you IF the instructor will very carefully monitor the second time the students work on your mower.
Basic mower maintenance is not rocket science. I'd suggest getting a few books from the library and doing some reading. You can save a lot of money over the live of the mower by doing the easy stuff yourself. If you spend the recommended $50 or so per year for tune ups and such, then for the 20 year life of a mower you are paying somebody $1,000 for some very simple work. Include monthly blade sharpening plus occasional maintenance such as throttle cable replacement or ignition system replacement and the saving are even greater.
Good luck, Gideon
===================
I had the local college kids give it a tune up and I suspsect that something was not done correctly.
I got the mower back from the college and I found that the blade was loose. I tighten it, mowed and stored for the week. The next time I tried to star ( a week later) the engine kicks back and yanks the cord from my hand.
I noticed that the oil was a little low so I added.
The blade spins freely. The cord is hard to pull and when the engine seems to want to start it yanks out of my hand. I also get a puff of grey smoke from the out of the air filter.
Any thoughts?