The driver door lockon my 01' Blazer is jammed when trying tolock/ unlockwith the key, and the passanger door key just spins 360 with no resistance. The remote entry still works, but is the only means of unlocking the doors from the outside. Any Ideas?

 

You could try spraying some liquid graphite into the lock and working it to try and free it up...

On the passenger side, sounds like something is broke inside the door. I'd pull off the interior panel and have a look at the key cylinder.

 

they have always worked fine, then one day they both were broken

 

Seems like a coincidence that both are not working, has someone tried to break-in to your vehicle using a screwdriver or a blade or something? Any signs of damage on the locks?
Make sure you have good batteries in the remote!

 

no damage. the remote works fine

 

Sound like the linkage has come off inside the passenger door and the driver door needs lubrication.