Poor starter, plug gets wet, starts when bumstarted

float in carb not shutting fuel off

Battery.?
Starter button issues.?
Poor quality wiring.?
Bad joints/connections on the wiring.?
Faulty starter motor.?

If plug is wet with fuel, it is likely flooded. A flooded engine will not fire... even with starter fluid.

Remove air filter and spray a short 1 sec. burst of starter fluid into throat of carburetor and promptly pull starter up to three times.

If still no fire, check if plug is wet. If wet, then likely flooded. Dump fuel from tank, remove spark plug and pull starter several times to clear excess fuel. Check spark plug gap and reinstall spark plug. Leave fuel tank empty and repeat above procedure. If still no fire, remove plug... it should be dry. If dry then either insufficient spark (fouled plug), timing (sheared flywheel key), or insufficient compression (probable crankcase leak).

Pull plug see if it is wet. Wet means gas getting to cylinder. Replace plug if worn. Check oil level and condition. Fill or change the oil. Ensure "deadman's cable is working. Spray starter fluid into carb at air cleaner to start. Ensure air cleaner is installed correctly.

Battery is defective if clicking is solenoid for starter trying to engage the starter. Did you get water under the hood, could also be wet ignition coil or distributor. Did you disconnect anything while getting at spark plugs like a wire to ignition?

Doubtful you have a fuel pressure problem if the car runs well, poor starting can be a few things , poor air circulation air filter needs cleaning or replacing, poor injector flow warn injectors or just dirty fuel additive sometimes clears this , poor spark plugs not firing under pressure ok when started . for diesel cars you don't say what car it is , poor glow plugs . bad fuel filter , air leaks in fuel pump , poor injectors . and especially with diesel poor compression due to worn rings or head gasket failure . You may even have just have disturbed the engine earth strap when you replaced your starter motor .

It is more likely to have poor fuel in the carberettors. I would start by removing the spark plugs and give them a sniff. See if the fuel is potent. Note if the spark plugs are wet. If they are, replace the spark plugs with Champion plugs and see if it will fire. Let me know if you need anything else.

i have found 2 areas that cause issues such as you are reporting.
one is poor voltage. check the connection at the starter motor between the alternator and the battery.
the other and perhaps more likely is a wet ECU.

the ecu box is under the windshield on the passenger side, access under the hood. this are can get wet ad corrode an ECU.

remove the ecu, take the bottom plate off and clean any corri=oded and wet areas with alcohol and a tooth brush..be gentle.
i would look for a way of mounting the ecu so that it doesn't lay on a flat surface that gets wet...

check cap rotor wires and coil. likely one or more of these items is arcing and causing poor spark distribution.

turn the engine over for at least a minuit in 2 or 3 intervals. (NEVER HOLD THE STARTER MORE THAN 25seconds at ONE TIME) pull out a spark plug or two and see if their wet and smell like gass, then you know if its getting fuel. You will need a long 3/8'' extension cuz its overhead cam but the front plugs are easy to get to. If the plugs are dry then pull all the plugs and poor no more than a 1/4 ounce of clean gass in each cylinder of your inline 4, reinstall each plug as you have added fuel connect the plug leads again and start it. if it starts momentarily you've varified the proplem. If the plugs were wet apone the first test verify you have spark, pull one plug & reconnect it to the plug lead touch the bottom of the plug to the engine block (away from its hole) and get some one to crank the engine darker the environment the better and look for a brightblue spark it should be their on all leads. Hope you find somthing