Wish I could find nearly new mowers lying around! A few tips which will hopefully get it going; Is there any fuel in the tank? If there is, it may be stale and useless. A quick sniff will tell you all you need to know. If there is, I suggest you remove the fuel tank (usually only a few bolts) and flush it out thoroughly with clean petrol. Do the same for the carburettor and fuel lines, since old petrol forms a sticky substance which bungs everything up! When done, refill tank with fresh petrol.
Also remove the spark plug and check for any damage. If none, give the electrodes a good clean with a small brush. An old toothbrush will do the job. Check that there is a gap between the electrodes. While the plug is out, give the start rope a few gentle pulls to check that the engine isn't seized. Be careful here - if things feel unusually "tight" there may be surface rust on the bores. To avoid the risk of breaking the piston rings, inject a little light oil (not too much though) through the plug hole, have a cup of tea, and try again.
If all is OK, replace the plug and try to start the engine. hopefully, after a few pulls, it will fire up. If nothing happens, remove the plug again. If it is damp and/or smells of petrol, fuel is getting through. It may then be that you are not getting a spark at the plug. Check this by putting the HT lead back on the plug, and earthing the plug on a suitable metal surface (cylinder head is ideal). Shouting now - DON'T hold the plug or lead with your hands; if the electrical system is working, you will get a hell of a belt when the cord is pulled. Not nice, believe me! Now give the rope a pull. There should be a nice fat spark, clearly visible at the electrodes. If so, put the plug back and try again. If not, there may be a deeper fault within the electrical system.
Give it a go, and let me know how you get on - if you still don't get a result, we'll delve a little further....... Good luck!