You gotta start somewhere. ^^^^ Compression test is first on my list of checks, too. ^^^^ If the compression test results in a reading of at least 100psi, the engine should be capable of running, unless the top end is torn-up beyond belief. Pull the expansion chamber (pipe) and look into the exhaust port. What's it like in the cylinder? Poke the piston with a popsicle stick. It should be firmly planted in the cylinder. A Blaster obviously won't start if it has a scored, burned, worn-out, or scratched piston/cylinder.
Do you have fuel to the cylinder? What about fire? Do a crankcase leakdown test. This test checks the engine's bottom end for air leaks. A missing/badly damaged seal or gasket will prevent the engine from starting. This problem may also cause the engine to kick over poorly, because there's no 'crankcase compression' present.
As you figure your new quad out, (congrats on the purchase, BTW! ) post what you find, and I'm sure the problem will get figured out...