Fuel filter, electrical wires, fuel pump
The first thing to check would be the fuel filter. It is cheap and easily replaced.
The electrical wires are also not hard to replace. To check, you can use a sparkplug tool, but you can also open the hood with the engine running in the dark and look for sparking. You shouldn't see any sparks. If you do, check the point at where the spark is arcing. Also, make sure that the wire is well connected and not corroded at either end.
Perhaps some fuel injector cleaner might clean out goo that is blocking your injectors.
The fuel pump is probably electric and most electric fuel pumps are pretty trouple-free. Mechanical pumps fail much more often. A fuel pump usually fails fairly rapidly once it begins to fail, because a small hole in the diamphragm tends to enlarge and then no fuel gets pumped.
I am not a professional mechanic, and not familiar with your specific car, but my approach is to replace the cheapest stuff first. I always try to buy the completely transparent fuel filters, because you can look inside without destroying it. Should it not be clogged, you can recycle it as a spare.
Semibodacious Transmogrifications a Specialty
1990 300D 2.5 Turbo sedan 171K (Rudolf)
1985 300D Turbo TD Wagon 219K (Remuda)
"Time flies like and arrow, yet fruit flies like a banana"