Have a toro 20074 electric start, charged the battery for a full day, started right away, cutting the lawn, stopped for a break, went to turn the key and nothing, I mean nothing, had to use the pull cord, checked to make sure the wiring was connected, no problem there, could that battery just die while your cutting the lawn?

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

The battery and charging system only start the engine. They have no affect on the engines running. The engine runs off magneto ignition which requires no outside power source. Check your battery for full charge with a volt meter. !2.6 volts is 100%. If the engine is hard cranking with a battery at full charge it could be valve timing, valve clearance, or the compression release not operating properly.
One other possibility would be the carb flooding an filling the cylinder and crankcase with fuel but you would have noticed smoking after you got it started had the cylinder been full of fuel.
I would start diagnoses by checking the valve clearance and check the flywheel key.

advise doing a compression test with gauge.

could be valve not seating or low compression

Battery charged? Bad fuel? Low on oil? 30w oil required. Clean carb. Check for improper ground on starting circuit. Ignition switch providing power to starter when key turned? Always use Stabile in gas. Remove bowl from carb ensure float is working properly. Float up no fuel flow, float down fuel flow. Ensure oil is full, low oil shutoff will not allow starting.

Battery required? Charge battery or replace. Replace air filter and spark plug. Dump out old oil and replace with 30w oil. Electric start may have a fuse blown. Dump out old gas fill with new with Stabile always added to gas. Try spraying starter spray in carb at air cleaner with filter removed. All mowers have a low oil sensor to prevent starting on low oil. Remove bowl from carb, should be full of gas. Pinch off fuel line with pliers or turn fuel valve off. Check float should be hanging down allowing fuel flow. Float up stops fuel flow.

Electric start engines are designed to recharge the batteries while running.

Check battery connections, make sure they are clean and TIGHT!
Check the harness where it plugs into the starter switch
Check the harness where it plugs into the battery wire harness
Check the cable at the starter, make sure it is clean and TIGHT
If you need it, you can go to toro.com and enter your model number and download both the Owner's manual and a parts manual if that helps you any

If you never used the starter,You need to have it checked, possible that it i froze up. Or brushes in starter arn't making contact. Also check connections. Good Luck

I pull the rope and it seems like it wants to start.It will not start with rope ? are you sure your brake control cable is adjusted right if not it could cause it not to start,you said after you pulled rope and trys to start you used it twice when ?