Tiller will not start

Remove carb and disassemble to soak in carb cleaner. read my other resolved questions for more info.

There are several things that will prevent a 2-cycle engine from starting. The most common causes are no spark or no fuel. To check for a no spark condition, remove the spark plug, connect it back to the spark plug wire and while holding the spark plug boot, ground the spark plug against some unpainted metal part of the engine - usually the head. Pull the rope starter and observe if the spark plug is firing. You may need to do this in a dimly lit place to be able to see the spark. If you do not have spark, replace the spark plug and try again. If you still do not have spark your coil might be bad or the magnets on the flywheel may be badly rusted. Either way you must remove the engine to service it and may want to seek professional help.
If you have spark, try spraying engine starting fluid into the spark plug hole, reinsert the plug and try starting again. If the engine runs for a few seconds and then dies, it is probably running out of fuel and you have a problem with the carburetor. Remove the carb and carefully clean it by taking it apart, spraying it with carb cleaner and using a small wire about the size of a sandwich bag wire tie without the paper. Reassemble the carb and try again. Also check the primer bulb for a pin hole and replace if necessary. Check the fuel lines to see if they are cracked and replace them as needed.
If you have both spark and fuel and it still will not fire, you may have a severely scored piston, rings, and cylinder due to not running the machine with the proper fuel and oil mixture. You can use a screw-in compression tester to measure the compression of the engine. If it is below 90, you may not have enough compression to allow the engine to start. In this case the repair is much more intensive and even though you can buy a new short block, unless you are able to do this complicated repair yourself, it would probably be more cost effective to replace the tiller. Good luck.

If you left ANY gas in the carburetor for more than 5 months the carb is trashed. Do NOT buy a rebuild kit, it won't work. You need to but a new carburetor. ALWAYS run the engine dry before storing for more than a few months. It took me two new carbs before learning this.

Check first whether you are actually getting a spark. Remove the plug, re-attach the spark lead and place the body of the plug in contact with the engine block. If the engine has a cowling which makes this difficult, you can use a socket from a socket wrench set or something similar to bridge the gap. Alternatively get an assistant to hold the plug against the engine with a plastic clothes peg. Pull the cord and check the spark is ok. It may be easier to see it in the shade or indoors (Don't run an engine too long indoors).
Problems with 2-cycle engines are often due to fuel flow issues in the carburetor. If the engine has a primer, make sure it is sucking up fuel. Look inside the tank and check that gas runs out of the return line when the button is pressed (the line without the filter).
Clogged jets can cause problems. These can be cleaned with a carburetor cleaning aerosol.
The valve in the gas tank cap can become clogged with particles of dirt. Check this is clear.
For a pictorial guide to cleaning a carburetor on a 2-cycle engine (used on string trimmers, chain saws, hedge trimmers and some lawn mowers), see my guide at the link below
String Trimmer Won Work 2 Stroke Engine and Carburetor Troubleshooting