I would make a list of possible points of failure:
Input
Timer
Pump
Pipe
Endpoint.
If you "unscrew" the sprinkler system and turn on the "pipe" do you have water flowing?
If you remove the "timer" and just connect the pump directly does the sprinkler work?
If you drop in a spare pump does it start working?
If you "cut" the pipe right after the pump but before the sprinkler endpoint do you have water flowing?
If you remove the sprinkler "head/endpoint" does it work?
It is entirely possible that you will have just rip out and redo the entire system.
How much will it cost you to buy a brand new
1) Timer
2) Pump
3) Pipe
4) Sprinkler Head
I found this random DIY sprinkler youtube
video, let me know if it is any good
https://www.youtube.com/watch?v=KyL-UrFKlzQ
Iterations are fine, we don't have to be perfect
My 2nd Location:Florida HardinessZone:10 AHS:10 GDD:8500 Rainfall:2in/mth winter, 8in/mth summer, Soil:Sand pH8 Flat