Sounds like the ignition module. Did you check it is tightly in place? If everything look tight and in place and you don't get spark, then that might be your problem.

Durable as Yungman has advised check you wiring to the Plug . A continuity rest with a multimeter will confirm.
Otherwise check your kill switch or a Coil Ignition Module may be as indicated required . If so most dealers have used (tested) Modules that you may wish to try 1st .

You may also want to check the air-gap from the flywheel magnets to the leg(s) on the ignition coil module. Most people set them the thickness of a standard business card.

I have two fairly new 26ss Homelite Mighty Weed Trimmers. Both have less then two (2) hours of running time on them. On one the pull string wont return, it wonÂt start the engine. I tried rewinding the spring and the string at least 8 times and I still canÂt get this thing to work right. I am an automotive machinist of over 40 years I work with the smallest to the largest engines all day. I had several other Top Machinists in the shop take a look at it as well. The string wont return back to its original position after a load is applied to the engine. After the second pull it jams again. The only other option I can think of is to replace the starter pulley. But the trimmer is new right????? I paid $120.00 for the thing new, and spent about $400.00 in time trying to fix it. The other trimmer the muffler fell off after the third (3) usage

Recoils can be tricky , all may look as it should mechanically , but a worn spring or bushing is all it takes to cause it to not properly recoil on these light weight units . Have you applied light grease or even better some WD-40 and try the recoil action off the saw. Most likely yes you have with your apparent technical experience . Since the unit is very new no chance of alternate guage or additional amount of rope being reinstalled . if all else fails you may have to visit a authorized dealer to compare (eyeball) a new recoil unit for comparision . As I said I have repaired many and some have looked great but either the spring was weak or binding was cuased by lack of lubrication on the spool thrust washers...etc .

Papa: As for the second Trimmer , size up your muffler fastener sizing requirements and ensure to apply a thread locker prior to reinstalling the fasteners. Numerous small engine units have vibration and thermal cycle loosening issues , either lock washer use loctiting or safety wiring resolves the issues .