I hate to tell you this, but you just bought yourself a mess!
If there is not a VIN plate visable on the left (drivers side) dash and you did not get a title, you have a problem.
First off, I would call the person who sold you the car and demand the purchase price back along with any incidential charges such as transporation, etc. You should also report this to the state highway patrol and have them come out and look at the hidden VINs on the car to see if the car has been reported stolen or if it was ever salvaged.
Just buying a title won't do you much good as you still don't know whether or not you actually own the car you think you own. It's a very real proposition that the car you have is stolen, salvaged or something else.
Not a pretty picture any way you look at it.