Briggs & Stratton Quantum 3.5 cannot start?

I have a Mountfield rotary mower powered by a B & S 3.5hp engine. It is quite old but been well looked after.

Took it out the other day for the first start of the year. Put some new petrol in, changed the oil, took the air filter off and cleaned it out (put new one in last year), replaced the plug because it looked like it needed it. Tried starting it and nothing. It looks like there is no spark.

There is no guide in the maual as to what to do next except contact the local B&S dealer. The response I got from them was that I should buy a new mower!

I don't think there is anything seriously wrong with it and I don't want the expense of buying a new mower. Can anyone give me an idea of what the problem might be and how to fix it?

Thanks in anticipation.