Testing For Salmonella in raw eggs
The FDA advises no more than 2 hours should pass between purchasing refrigerated raw eggs and putting them back into a refrigerator. 2 weeks exceeds that by 168-fold. Toss those eggs and purchase new ones.

There is no easy at-home test for salmonella, and certainly none as cheap as a carton of eggs. If you want to completely avoid the risk, I would recommend finding a source of pasteurized eggs. Barring that, get new eggs from the store and follow all FDA advice regarding their storage, handling, and cooking.