forget compression test for now...
First thing to check is does the pump prime when you turn the ignition on.
You should hear it but if not you can take the fuel pipe off the fuel rail, put the pipe into a cup or something and cycle the ignition, it should prime and fuel come out (will come out fast but only for a second as it primes).
If it doesnt then you need to test theres actually power going to the pump with a multimeter, you can also check the earth side as well. How this works is the ecu tell the pump relay to activate, which sends 12v to the pump, the earth side is just straight to earth but through an inertia switch so if theres no ground the inertia switch could have activated (not likely so won't go into that, just check theres aa earth with at the pump connector and 12v on the other). I dont think itll be the pump so i'll stop there with pump testing.
Assuming the pumps priming, now test for spark. Whip out a spark plug, reattach the ht lead and lay the plug on the rocker cover. Turn the engine over and watch for spark. You can check a plug thats powered by the other coilpack to be thorough.
And also for fuel, few ways to do it but i'd grab a test light or a multimeter and just probe across the 2 pins on the injector connector - test light should flash, a meter should show a pulse on DC volts. This proves the ecu is telling the injectors to fire, not that they are actually injecting - in most cases this is enough to go on. But you can also just crank the car over a lot and then quickly whip a spark plug out and see if its wet and smells of petrol or not.
So at this point you should know if fuel is at the rail, whether you have spark and whether you have fuel. Let us know the result.
Likely issues are crank sensor or twin relay (otherwise known as fuel pump relay but it fires the coilpacks too) for a car cranking and not even attempting to fire. But far from the only possible reasons. Hence checking for fuel and spark.
Does the engine management light behave as normal? Its the one that looks a bit like a hose pipe squirting water, it should come on for a moment with the key and then go out. Same for the immobiliser code light, should come on for few secs and then go off, if it stays on the immobiliser is armed and the car wont start.