You need to get busy with a multimeter. Remove the side controls cover. Looking at it, do you have a large PCB, or a collection of relays?
If relays, unplug each one and replace just to eliminate any poor connections. If a PCB, then carry on thus. Switch on and check for power to the fan terminals, if you have none, then check the thermostat for power feed and supply. If you have power and the fan does not run, raise the air cover at the top and try moving the fan with a flick of a screwdriver. If the fan starts you need to check the pressure switch is operating from NC to NO. If it does that, then the next phase of operation is to check the transformer feed. You can usually check the glowplug for localised heating round the body. After about 2 mins, you should hear the pilot valve open the fuel should then flow to the pilot pipe and get ignited by the glowplug.
If you have run out of oil, you may need to prime the pilot feed. Undo the connection into the burner and use a piece of tube over the open end and when the pilot valve operates suck fuel through. If you cannot suck, then the pilot solenoid may be goosed.
If the pilot lights (you can check this by removing the thermocouple and looking through the hole. If it lights, replace the Thermocouple and after a short time you should hear the main valve open.
At each stage, check the appropriate terminals for power.
if the pressure switch does not work, you may have a choked up boiler. When was it last serviced?
I would never recommend a reconditioned cooker with boiler. The burner may be OK, but you don't know how good the boiler body is. I've seen recons fail within 2 years.