I had a similar problem on my small motorsailer recently after it was laid up through the Winter and not run for some months. I drained water from the seperator before first starting and also checked for signs of diesel bug. I have had it perviously on this boat and it is easy to spot as it looks like very fine gloopy mint sauce.
There were no signs of bug, so I attempted to start the engine, which fired up and ran for a couple of minutes before slowing and stopping. It then fired a couple of times but wouldn't run. The fuel filter was checked and I found quite a bit of water contamination, so emptied it out, flushed it with meths and manually refilled it with fresh diesel. The engine fired again and ran for about 2 minutes.
I then bled the whole system and checked that the lift pump was working but to no avail, so checked for fuel delivery anf finally found that no fuel was coming through the tank on/off supply tap. I ended up taking the fuel supply upstand pipe out of the tank and found that the bottom end of it was completely blocked. It was also only about 4mm from the bottom of the tank when in position, so I guessed that it had picked up sludge and sediment from the bottom of the tank over a long time. I sawed an inch off the pipe, used an extractor to get out as much muck as possible and reprimed and bled the system. It started immediately and now runs smoothly and sweetly.
EDITED TO SAY that a partial blockage may still allow the engine to start and run at low speed or on tickover, but with not enough fuel to keep it going when revs are increased.
Finally, if you do find evidence of diesel bug, it is not neccessarily as big a problem as is often feared. Over 8 years of having the boat and leaving it standing for long periods, I have found the bug on 3 occasions and each time cleared it with Marine 16 or Starbrite diesel bug treatment. With both products it worked in about 3 hours, although you need to make sure that you put a drop in the filters etc to kill anything in the lines. I now always leave treated fuel in the tank over Winter and have remained bug free for the last couple of years.
Roger