Horrid shades of the past.....
The cheap-o lead-acid battery (the one with refill plugs like a motorcycle battery) won't turn the engine over unless it's, as previous stated, on a brand-new charge - period. When you get some spare bucks, replace a lead-acid with a gelcell lead-acid - also, no maintenance, eh?
With that said, is that the only problem? It just won't turn over? I was always proud to hand-start my engines. It's a skill that brings you right up-close and personal with your engine. Unless the engine is some sort of weird high-powered thing or totally played out, it'll hand-start, and it's pretty easy once you have yourself and the engine trained. Try it!
Once the starter fails to turn it over, can you turn it over by hand? If not, you're flooded. If it'll turn over by hand, then you need a new battery. My two sense