This is a carb engine right? How did it run when you got it last year? Cold starts OK?
The things I'd look at are the fuel filter (the big water separating filter, looks like an oil filter). When you remove one of these be careful because it will be full of gas. There is an anti siphon valve on the fuel tank fitting that the fuel line is attached to. I always shut off the battery switch when changing fuel filters, just in case something crazy were to happen (ie wrench falls across batt terminals, wrench shorts between starter solenoid B+ and ground, not likely but ya never know).
I use an oil filter wrench to remove these. Then get a large Mason jar and pour the gas into it and let it sit. Look for a layer of water on the bottom. When replacing, first put a coat of motor oil on the gasket or else it may be stuck on there next year. Then I fill it most of the way with gas to make it easy for the carb to prime. Just hand tight. Not gorilla tight. The carb may have a filter in the inlet, I know the Rochester 2bbl and 4bbl ones do, not sure about the Holleys used on later models than mine.
But first, make sure the choke system is working right. It is a prime suspect in any cold start problems. When you remove the flame arrestor you can see if its working right: advance the throttle all the way, then move it back to 1/3 or so. Cold engine the choke plate should be closed or almost closed. If not clean the linkage with carb cleaner. When the engine starts, the vaccum break or choke pull off should pull the choke open a fraction of an inch, to give it enough air to keep running. If it does not close nearly all the way, or it does not open a bit just after starting you can have this problem. Be careful running the engine without the flame arrestor installed.....
What engine do you have? 5.7? I looked this up in the OMC parts section on Crowley Marine's site, keep in mind that OMC and Volvos were identical from 94-98/00 for most models. Volvo's site is a nuisance to navigate unless you have a model #. Anyway the carb looks to me like a Holley 2 bbl.
http://www.crowleymarine.com/johnson-ev ... mdl=INSV6KTwo things I noticed:
1) it uses an electric choke...these close via a thermostatic spring but open via timed choke heater element. If the linkage has dust n dirt on it it may not close. If the element failed or has no electric power it will not open as the engine warms up.
2) no separate fuel filter at the carb inlet that I can see like my Q-Jet has. So the big water separating fuel filter is it.
Post back what engine you have (I'm just guessing here) and we can help more....