the fact that you have 2 symptoms (no sparks... no start) would indicate it would be a very bad lucky situation to have a bad selenoid.
selenoids are simple devices with a single internal coil to magnetically close the starter circuit .
the control wire should show 12v while in START mode while the other side is grounded either internally or by a wire direct to ground or via a safety switch
the selenoid should click
I suspect you have no 12v feeding the relay since the same12v is missing on the ignition circuitry (no spark)
before spending to much money on selenoids you should try to hunt down the missing 12v
you can test the selenoid operation by directly applying a fresh 12v on the + control post
btw make certain +12v is reaching you key B+ post and the key is internally transferring +12 to the ignition, choke and start posistions
another issue is improprer ground of the engine frame itself. you could have all the 12v in the world with nowhere to go if the engine and grounded components are not "grounded" to return the current flow back to the battery NEG post .
inspect all battery cables connections for oxidation or bad crimps . Clean up all connections. battery end and engine end
you could also test by having a buddy holding the key on START and poke around by bending accessible wires, tapping around to detect any loose or internally broken/oxidzed wires. turn the engine side to side while in start mode.
Intermittent problems area pain Hard dead is usually much simpler
