The first thing to check on failed STI levers is the cable. It can be broken up in the housing an not be obvious. Test by drawing it away from the down tube like a bow string and see if you suddenly pull down tons of slack indicating a break. If not try shifting the lever against that same tension.
If the cable seems OK, it's possible - especially on levers that haven't been used for a while - that dried, or hardened grease is keeping the small spring loaded parts from moving freely. Cross your fingers and say a prayer because this is the easiest and cheapest problem to fix.
Spray the mechanism with solvent ot super thin lube , like WD-40, LPS-1 or whatever you have to dissolve and flush dried lube. Rest it a while then work the lever and see if it comes back to life. Dry it as best you can, and oil with a light oil, and consider yourself lucky, because most actual mechanical failures are not repairable, and these levers aren't cheap.
__________________
FB
Chain-L site
An ounce of diagnosis is worth a pound of cure.
Just because I'm tired of arguing, doesn't mean you're right.
“One accurate measurement is worth a thousand expert opinions” - Adm Grace Murray Hopper - USN
WARNING, I'm from New York. Thin skinned people should maintain safe distance.