I usually work on gas burners but can hopefully provide a few pointers (do occasionally work on oil).
The power will likely come through the stat and over temp stat sited above your burner (to reset the over temp, unscrew the cap and push in the button), then to the control box base. Check for power.
If OK, re-seat the control box, ensure it's pushed fully forward (also check all cables in base are secure and that none are broken and that base to box connections are clean). The wiring looks correct (obvs without tracing it back).
The clicking you could hear was the control box going through it's sequence to combustion (pre-purge - ignition - fuel - check flame)
A few observations - it looks like the pipe to the air damper ram has been crimped over (which is probably what's keeping the damper open).
the valve in front of the burner is a fire valve and has a fusible link inside which melts when it gets hot to interrupt the oil in the event of a fire, this is easily broken if wound forcibly in.
Before you attempt to fire it you should check the oil flow by removing the flexi from the pump (turn off the valve at the tank first). There should also be a filter somewhere in the oil line - this will need replacing probably.
That flexi should ideally run below the burner, not over the case.
Here's a cheat sheet I did a while ago:
To check photocell, remove from control box. Re-fit control box and fire up burner. If it fires after 12 secs and then locks out after 5 secs, the photocell is faulty.
Check continuity of the blue and brown wires and blue and black wires of the solenoid coil. If no continuity, then replace coil.
Check voltage on white wire to terminal 7 of 530 SE control box. This should be 50V AC +/- 3 volts.
If no voltage present, change burner motor.
As a last resort, change the control box 530SE.
And i've hopefully attached a fault finding chart:
HTH