i have a astra 1.7 s reg van that doesnt start first time?

hi there
ive recently purchased a 1.7dt1 s reg astra van
when trying to start the van it turns over but doesnt fire up,it will after a couple of trys but ends up flattening battery,its been in a garage for a couple of days and the mechanic has checked glow plugs and has rung me to say it might be the diesel pump,
does this sound right as the van runs sweet when fired up and this is going to end up an expensive might be!!