Maybe - was the A/C switched on when you tried to start the car? You mention a recent new alternator. I suggest you take a close look at the accessory belts and make sure they are all still on the pulleys. Either a seized accessory or a belt that has come off and is now wrapped around something would account for all the symptoms you describe. If you have a handy helper, get him/her to watch all the belt driven devices under the hood (from a safe distance) while you try to start it and see if the pulley is not turning on one of them.