The problem is definetly in the fuel system. You might have gotten a bad tank of fuel which has a lot of water content in it and very likely. I don't know if cars have fuel/water seperators or not so check if your car has this. Really the only thing you can do besides draining the fuel system is to drive the car near empty and wait a few miles to replace the fuel filter. But, before you do all that, if you can reach the fuel filter yourself, see if you can tighten it. If you can, take it all the way off and make sure that the gasket is there and in one piece but make sure you don't drain any fuel that is in the filter. Dry the gasket area off as best you can and put a light coating of engine oil on the gasket and then put it back on. As long as you didn't loose too much fuel out of the filter you will not have to prime the fuel lines. If you had or have any substantial amount of air in the fuel system your motor will lack power or not run at all.
But, if you really trust yourself with a wrench while you have the filter off (this is really easier then it seems). Get two clean containers. One, one gallon container to put fuel in the filter, and one small, clear or white plastic container. Dump all the contents of the filter into the clean, plastic container. Diesel fuel is heavier then water so you will see an off-clear liquid in the bottom of the container and then what looks like clear bubble(s)on the top. Now, a lot of tiny little bubbles in the center right after you pour all the contents out is OK, and a lot of little bubbles that migrate to the outside edges of the container are harmless tiny oxygen bubbles. But, a big blob of clear stuff that looks like air is actually water that has surfaced to the top (You might have to wait a while for the water to surface). If the clearish bubble is more then a few tables spoons then you got a bad tank of fuel and the only thing you can do, that is not costly, is put clean fuel back into the filter and then put the filter back on the car and then drive the car everywhere you can to actrually waste fuel before you make the trip back. If you see no blobs of water in the fuel then I would suspect that the filter is bad for some reason - probably a microscopic hole in the caseing of the filter or gasket. If so, get a new filter and top it off with clean fuel, grease the gasket and tighten it back on the housing.
In a very basic way, diesel powered motors need only two things to run: cleanish fuel and air. As opposed to gas powered things, diesel powered things only need electrical energy to stop the flow of fuel to shut down the motor. Whereas gas powered motors need a spark to ignite fuel. Compression that causes friction ignites diesel the fuel.