Good grief. Just take it to an oil change shop, Jiffy Lube, whatever, and have them do a radiator flush. Just tell the tech to run the machine 'til it runs clean, then drive it home and swap the radiator.
I'm all for doing everything yourself and saving a buck, but, if you don't even have access to a hose you're not going to do a very good job of it. With the situation you're in paying for a real radiator flush would be the much better deal.
