Engine stopped when using and now won't turn over I have charged battery still nothing

604 is not a complete model number for MTD. However, it looks like you may have the following machine which was manufactured in 1991. MTD 131-604-000 (1991) Lawn Tractor

Found Manual for Model U604H
This manual also for: M3800s-bn.
Download manual

Do check the oil or see if you can manually rotate the engine. Be sure you did not overheat the engine and cause it to freeze up. If this has happened none of the rest of this post is going to help.

Your problem sounds like a Key Switch failure. The Key switch is the one component that the starting circuit and the run circuit have in common.

Note: If you have a good electrical diagram and an ohms meter you can test the Key Switch directly. However these tests let you test the switch without a schematic. They should work on any riding mower.

You can test this theory by jumping the starter. Hold a wrench or fat screwdriver across the two large posts of the starter solenoid. This bypasses the key switch and directly drives the starter. Your starter should crank. Don't crank it for more that a couple seconds. You just want to verify the battery and the starter are both in good shape.

If the starter cranks try one more test. Run a small jumper wire from the positive post of the battery to the little terminal on the solenoid. You may have to remove the small wire off the terminal on the starter solenoid in order to do this. When you apply this current from the battery to the terminal it should make the starter crank. This test bypasses the key switch and shows you the entire starting system is working. You could do this test first and if it works you do not need to do the first test.

If these tests cause the engine to crank, odds are high the key switch is bad. If you want to do a further test to verify this do the following.

Consider the engine kill system. Modern day safety systems include a kill wire. This will be a single wire going to a connecting terminal on the coil (magneto). The wire is small and can be disconnected from the magneto. Disconnecting this wire isolates the engine from all the possible bad switches, relays, diodes, and wiring setup designed to kill the engine if safety procedures are not followed.

With the kill wire disconnected the Coil functions entirely independent of the rest of the wiring systems on the machine. If you disconnect the kill wire and the coil is good you will get spark to your engine regardless of the condition of the rest of the entire wiring system. Disconnected the Coil works all by itself; it does not need the battery or the key switched on.

You may need to remove the fan shroud in order to perform this test. You must find and disconnect the kill wire. You do not need to remove the shroud if you can find the wire that comes from the magneto and disconnect it from the rest of the system. Otherwise remove the shroud and disconnect it directly at the magneto.

NOTE: Many systems have a fuel shut off solenoid. This is a small black cylinder on the bottom of the carburetor. It has two wires running to it. This fuel solenoid will likely not work if your Key Switch is bad. If your carburetor has a shut off solenoid you will have to poor some fuel into the carb before performing the rest of the test. After poring in some fuel set the throttle to fast run, not choke.

Once you have disconnected the kill wire, then jumper the starter solenoid like before. Run a small jumper wire from the positive post of the battery to the little terminal on the solenoid. This is going to crank the engine. Unlike the first test we want to continue to crank the engine until the engine starts. Please do take the solenoid wire off when the engine fires or you will damage your starter. With the kill switch disconnected from the magneto and the starter solenoid jumped to crank the engine, if the engine is in good shape and has fuel, IT WILL START. This combination test definitively identifies a bad Key Switch. Replace the Key Switch.

Note: it is likely, with a disconnected kill wire the engine may start, but when you turn the key off, or otherwise try to shut the machine off, the engine will keep on running. Just slip the kill wire terminal back on and the engine will die, or wait till it runs out of fuel, or short the kill terminal to ground.

Better check oil. Check the under deck. grass buildup or a stick or etc.