Should I just haul my bike to the dealer or is this something I can sort out myself?

Based on the description of the dark, damp plugs and the fact it won't catch, you are almost certainly dealing with a fuel issue, which is the most common problem when a bike sits through winter. Since it's a cruiser and you mentioned a weak smell of gas, the primary suspect is old ethanol-treated gasoline. Even if the tank was only a third full, that old fuel probably broke down and gummed up the small orifices in the fuel system, including the carburetor jets. Just sitting for five months, even with a nice tank, can turn high-quality fuel into sludge that prevents a proper burn. Regarding your plan to try fresh fuel and new plugs, that's exactly the right first step. Drain the fuel in the bowl and refill the tank, but when you do that, consider trying a fuel system cleaner mixed into the fresh gas. This helps clear out any remaining gummy residue.

As for the carb, trying to fix it yourself is feasible if you have the tools and a bit of patience. For a basic V-twin carb, you usually only need to check the idle mixture screws and the pilot jet. If the plugs look wet and you're cranking, it means fuel is getting to the cylinder, but it's not atomizing correctly or there isn't enough in the bowl. The dealer is overkill unless you confirm a deeper internal failure, but for most cruisers, a basic carb cleaning is a typical driveway job once the bad fuel is out. If the plugs look black and wet but won't ignite, check the fuel filter if it's accessible. Sometimes debris from old fuel can clog that before it ever hits the carb. Also, since it's a 2009, verify the ignition system components aren't fatigued from the cold. A weak coil or a faulty spark plug gap could cause misfire, but the fuel system is my primary bet.

I agree with the diagnosis that this is probably a fuel system thing. I dealt with the same issue on a cruiser a while back. Even after swapping out the gas and pulling the plugs, the problem stayed until I replaced the inline fuel filter. The old fuel just sat and gunked up that small filter before it ever got a chance to reach the carb. Check that part out too.

Try this before you touch the carburetor. If the fuel is fresh and the plugs are still wet when it cranks, the issue might be air. When these V-twins sit for months, sometimes the vacuum lines just go soft, or the air screw settings drift. Most people skip this, but if you just swap the gas and don't check the intake vacuum or the air idle screw, you'll just end up with a new rich condition. I had this on a Harleys, and the simple fix was just tightening a cracked vacuum hose before the fuel started leaking into the crankcase. Check the intake seals and make sure everything is airtight. Also, if you are swapping the plugs, make sure the gaps are set exactly right, not too wide and they won't ignite even if the fuel is perfect.

I still think the focus on vacuum lines is maybe a bit too complicated for this situation. If the plugs are genuinely wet, you have fuel in the cylinder, and while a vacuum leak can cause a stumble, it rarely prevents ignition completely in a V-twin like this. It seems more likely that the old fuel has physically gummed up the cylinder walls or the piston rings, leading to a lack of compression instead. Checking the fuel system and the spark first makes way more sense than hunting for air leaks after the gas has already been swapped out. A compression issue would give you that wet, cranking feeling without any specific indication of a vacuum problem.

I'm not sure about the fuel filter, but since you have wet plugs, we need to check if the engine can even fire with the fuel present. I ran a compression test on my previous rig and found that sometimes the injectors get fouled and the cylinder pressure drops by nearly 10 percent when they're cold. Try pulling the spark plug and spinning the engine by hand to see if you feel that same resistance on both sides. That will tell you if the problem is internal, not external, and save you from unnecessary carb work.

Update: I went with draining the fuel bowl and replacing the filter first. It was a bit messy, so be careful when working on gas lines. The old ethanol just clogged things up, but the engine is running smoothly now. It turned out to be a simple fuel issue.