Just thought I'd add to the knowledge base. I have 2 2004 V70s with 5sp.
Same issue each car 2 years apart.
Turn the key to start, the car fires momentarily then dies, rinse repeat.
1st car I was on the road so the hook took it to a local indy. Problem was the fuel pump control module died. They hide on the passenger side on top of the gas tank (plastic).
2 years later same same with the other car. This time I'm at home. Pressure gauge on the fuel rail and I get 10 psi. I hear the pump run twice then nadda. Fuel pump module again. Took apart the old one and I believe it's corrosion from the heatsink that kills it. Volvo PN is 30769225.
I hate SUVs and minivans and the V70s carry lots of gear or did I mention there were sticks :)