I have a Cannondale M600 Red White & Blue. My 7 speed Shimano integrated trigger shifter will no longer function.
Looking up the M600 on Bicycle Blue Book, it seems it was outfitted with Shimano STX SE Rapidfire shifters to work the 3x7 drivetrain. A Google search of "Shimano STX SE Rapid fire Shifter" yielded several results, including many videos on fixing a problematic STX shifter and it's rapid fire cousins. You dont describe the specific problem with yours but often with these types of shifters, the pawls become stuck with old dried grease and dirt and thus the shifting is unreliable or non-existent. Removing the cover and dousing the innards with WD-40 or similar degreaser while working the levers will clean the mechanism, freeing up the pawls, restoring their motion, and the shifter begins to function anew. Follow up the cleaning with application of a better lubricating spray grease and you may have a reconditioned shifter to use. Details can be found in several videos offered by search engine. Here's one such video.
Should you want or need replacement STI's, Shimano's current and readily available model, ST-EF500, is a 3x7 set-up and would be a drop in replacement. However if it's original, stock equipment you must have, the same search as above contained hits of the STX for sale, even a couple NOS (New Old Stock).