The first thing to check is the spring under the space bar - make sure it is not stretched, bent or something.
Also check the space bar stabiliser wire is properly in place.
The keycaps will probably clean up quite well, depending on what is on them. Are they 1 piece or 2 piece? 1 piece are trivial to remove and clean, 2 piece only slightly more so. Soaking in warm water with a couple of denture tabs usually works for me.