Car won't start checklist....

[Semnoz]

All of a sudden, car won't start

Last Sunday, I noticed it was slightly slower to start, but ran perfectly for 100 miles (as always). Yesterday (Tuesday) started fine during the day (2 times) and then took about 3 seconds to start later that evening. And then once home, it wouldn't start at all (glad I got it home then), and then tried a couple of times this morning and it still won't start.

I'm aware of numerous info out on the web, and have trawled through it, but would like some advice on a logical order in which to eliminate the cause.

Symptom: Engine turns well (battery is in good condition) but doesn't ever fire. No error messages. No leaks or any visible issues around engine bay.

I don't want to start replacing parts in desperation, in case it introduces another problem, e.g. if I replace fuel filter, I could create air-block, or if I change glow plugs, I might damage an electrical cable.

What would be my first check ? As the engine has always run perfectly, can I rule out the fuel pump, or can that suddenly fail ? If so, is a valid test to disconnect the fuel line, crank the engine and see if fuel spurts out ?

Is there a single component that can prevent the engine starting ? I'm aware that for each cylinder, parts such as inject heads/glow plugs can fail, but I'm assuming they would only lead to a very rough/spluttering engine, and not one that fails to fire up at all.

Sorry for all the questions on what is probably a common occurrence. I need car this weekend, and it's currently stuck on driveway, so I must fix this myself A.S.A.P.