FYI, The turn signal blinker unit under the seat works on resistance (and the heat made by it) to blink the lights. If the lights arnt drawing enough power through the blinker (or there isnt enough going in) then the lights dont blink.
So first of all, check to see if all four blinker bulbs work.
I'd also go around the bike checking to make sure all your wires and such are tightly connected, and that the battery connections are good. The express will run just fine with no battery, but then your blinkers dont get enough power and your bulbs burns out. Bulbs dont burn out from lack of current BTW, but rather from the unstable current coming directly from the magneto.
With that in mind, your battery has most likely eather gone pretty much dead or come disconnected somewhere.
Bottom line is to give the battery a good charge and check your connections.