We don't know what you should do. We can only give you suggestions.
SparWeb summed this up pretty well with this statement. Grid-tying car alternators is an exercise in futility. A "single marine deep cycle that only puts out 35 watts" means the battery can only deliver 3 amps. This, I don't understand. If the grid-tie inverter is one of the Chinese plug-it-in-the-wall type, then it's not a viable (or even legal) grid-tie setup in the first place. If the inverter is a real UL1741 compliant grid-tie unit, and you have a good wind resource (which it sounds like you might), then spending the money on a decent wind turbine is probably worthwhile. But no matter how you cut it, you're going to have $10 Grand in a real grid-tied wind turbine that generates enough power to make the project worthwhile.
With grid-tie systems it's all about money and payback time on your investment in equipment. If the equipment doesn't generate enough power to pay for itself, then it's not worth having it and you may as well buy power from the utility. Grid-tie systems typically don't pay off because it's more expensive to generate your own power than it is to buy it from the utility.
So, like Spar said, we can't tell you what to do. And when it comes to suggestions, I know of no viable wind power systems designed for grid-tie that are going to be able to be done for less than about $10 Grand by the time you buy the inverter, wiring, tower, turbine itself and go thru all the inspections and requirements by the utility to be able to do it.
If you're off-grid, or have grid power and are building an off-grid battery backup system to compliment your grid power and run some circuits in your home, then it's a different ballgame and there's lots of options. But that's evidently not the case here.