If somebody took an egg and smashed it into the vents at the base of the hood of my car, causing my A/C to smell like rotten eggs in the summer heat, and I was almost 100% sure I knew who did it, but couldn't prove it, could I get them in trouble anyway? What could happen to them?

When a person damages another person's property it is possible to sue that person in civil court to recover the cost of the damages.  However, the person who brought the suit needs to be able to prove to the judge that the damage was caused by that person, otherwise the judge will not make him pay for the damage that was done.