A few weeks ago on my 99 Disco1 110,000 miles I was having hard starting problems. I changed the fuel filter and it seems to have solved the hard start problem but now after I start the vehicle it seems like it wants to die. I press the gas and the rev's don't really go up. Is this the fuel pump or where should I start to solve this problem? Thanks.

 

Yes it could be the fuel pump. Driving with a clogged fuel filter will over work the pump and can burn it up.
I think that you can rent a fuel PSI tester at AutoZone, there is a schrader (tire) valve on the fuel rail, test the PSI and see what it is.
I am not sure what the fuel PSI is supposed to be on a DI.

 

Pretty much what Spike said, the valve in on the passenger side on the fuel rail. It looks like a tire valve. PSI should be around 40 psi (37-38). But that can be tricky too... If your pressure regulator is bad, it can let all the pressure back to the tank in the return line. The regulator is located on the driver side right behind the plenum, it has a vacuum line on it that runs to the plenum. But it is probably the pump like Spike said.