I used to have similar problems. Every spring the lawn screamed to be cut while the mower refused to wake up from hibernation. I started using Sta-bil gas and my equipment always starts with just a few pulls now.
Gas can 'look' just fine but that doesn't mean anything. If it's been sitting around for more than a few months, it deteriorates. I hate quoting an advertisement, but they're right and I'm too lazy to find authoritative proof. From
http://www.letsmow.com/sta-bil.html" web site:
Any fuel, be it gasoline, diesel, or heating fuel, is made up of many different organic compounds. These compounds are constantly changing over time and become new compounds that change the characteristics of fuel. Oxygen and other elements in the environment create new molecules that build up to form gummy residues or varnish-like films that can clog fuel lines, carburetors, and injectors.
I'd suggest changing the gas, but that doesn't really fix things. There's still gas in the carb bowl you can't get out, and the extremely small holes in carb jets could already be gummed up and plugged. Nevertheless, changing the gas would be a good first step. Also, putting a carb cleaner into the gas might help if you can get it started. That may help clean out any deposits.
http://www.goldeagle.com/sta-bil/faqs_stabil_detail.asp?product=sta-bil&ID=83" adding an octane booster such as 104+.
If the engine starts, you should fill your tank with fresh gas and use a fuel injector cleaner product (such as 104+ Octane Boost). If your engine does not start, then you will need to seek a professional mechanic for cleaning and repairs.
You might also check out the other
http://www.goldeagle.com/sta-bil/faqs_stabil.asp"
I can see how that can help, it adds exactly those components to the fuel that are most likely to oxidize or evaporate over time. Fuel is made up of a variety of hydrocarbons, and it's the lightest ones that are missing in old gas because of the reaction with air or simply because they evaporate. The rest of the advice on that page is sound too. If it still doesn't start, taking apart the carb and cleaning it is the only solution but that's not easy because the jets in the carb are so tiny. You can't simply shove a pipe cleaner inside, the deposits need to be disolved away.
Moral to the story is to use Sta-bil every fall when you put away the mower. Also put it in any gas cans you may not use for the winter or other equipment that is only used seasonally.