Many of these small engines have a kill wire that is grounded when the throttle is fully closed, which grounds the coil and kills spark.
make sure the insulation hasn't worn away.
IF still no spark, remove the shroud and manually disconnect it.
IF still no spark, bad coil is likely.but....
Remove it and clean the mounting area to make sure the coil itself has a good ground.

IF still no spark, new coil is needed.

It's a good idea to post the engine Model & Type numbers.
Quantum doesn't really mean anything. Telling us it's painted RED is about equal to the usefulness of knowing it's a Quantum.

This post was edited by bill_kapaun on Tue, Sep 16, 14 at 15:56

Bill,
Excellent advise.

it is a model 12h802 type 1767-B1 engine

Thinking about it a bit more-
Don't some of the newer mowers have a kill if the handle is released?
I have a 25 year old Honda with BBC, so I'm not up on the "new stuff".

I recently had the same problem with my 15 year old Toro Personal Pace mower with a Briggs 6 HP engine.
The engine has ALWAYS started on the first pull for 15 years.

I cut the grass and everything was fine. Put it in the shed and a week later I go to cut the grass and it won't start, no spark at all. I checked the wiring, all was well. Next I cleaned the flywheel magnets and the coil with steel wool, then reinstalled and set gap to .010". I also checked the flywheel key to see if was sheared but it was ok. Next I disconnected the ground wire going to the coil and still no spark.

I bought a new coil on Ebay for 20.00 shipped, installed it and fired right up as always. I would have thought there should have been some kind of symptom before it died but there was none.

thats exactly what I just did, order a new coil, nothing else adds up except a bad coil