Have you tried the following? When the front mech does not shift properly, I work down the list to see what is the cause.

1) Push on the front derailleur itself, the easiest point is the pivot arm where the cable is pinched. Can the derailleur move back and forth.
- If the derailleur cannot move, something is seized or broken
- If the derailleur moves, but does not snap back into the lowest gear default setting, spring might be gummed up

2) Try pulling on any exposed front shift cable, can you get the front derailleur to move back and forth and change gear whilst you rotate the pedal?
- If you can get the front mech to move and shift gears, problem is not the derailleur or cable/housing but the shifter itself
- If the front mech cannot move, even when you pull very hard on exposed shift cable, the cable itself is most likely seized within the housing due to corrosion

3) Push and click through your shifter, is the tactile feeling positive? I only do this step after I have gone through step one and two.
- If the pawls are not catching properly, shifter might be gummed up and need a solvent flush and relubricate
- If you feel the pawls catching and releasing normally, most likely a cable/housing issue. For example a worn cable and housing or cable tension is too low.