Bad battery or starter

No wires are needed to engine to make it run if magneto ignition. Now to stop you will need one wire to a ground in switch. Electric starter require 2 wires directly from battery with a solenoid on the positive wire and one low amp actuator wire to it from ignition and must be grounded common with engine is best.

That's a pretty common problem on small engines, but I never heard of brigs and stration! If that really the name, I am surprised that the real Briggs & Stratton did not sue them for trademark infringement, since it looks somewhat similar!

just turn the engine till one valve opens and adjust the other one and repeat with the other valve

Is the noise you hear actually the solenoid popping or the starter gear jumping into the flywheel?? You say it finally starts so I am guessing the starter is engaging and actually bumping the flywheel a little. If that is the case it is probably a dragging starter or weak battery. First thing is to be sure the battery is fully charged then see if it will turn over easily. If not you may have a started problem.

From your description it seems that the starter is not engaging to turn over the engine. First ensure all the connections of the thicker cables to the battery, starter and tractor frame are clean and tight. If starter motor is turning but still not engaging it will mean that the pinion on the starter motor is binding on the shaft. You can buy a new starter pinion gear from your local B & S agent.
To replace pinion, remove starter motor from engine, remove old pinion and put on new one and reattach starter to engine. If fuel & spark are right you should be up amd running.

Replace the battery. Even though the battery may say it's good, it doesn't have enough of cranking amps. Go purchase a battery with 350 cranking amps. This will fix your problem. The battery power isn't enough to kick the starter completely up to turn the engine.

check to see if the fuse is blown. or it may be the solenoid is bad. you can take it off and check it. if the solenoid is bad it wont get power to the starter

Unfortunately it sounds like you threw a connecting rod in other words a blown motor. The connecting rod has become disconnected from the crankshft and is jammed up between the case and the crank itself, the engine must be dissasembled and rebiult.

Im sorry but your motor has went to motor heaven,and most of the tme its cheaper to buy a new motor than it is to repair it and bring it back to life,

my mtd lawn mower wont start . when I turn the key there is a buzzing soung where the battery conectors are near the shifter but the starter is hot and getting juice