I lost my key to razor mx500 electric dirt bike how can i start it without key?

If the lights on a the throttle are showing a full battery then try disconnecting the brake switches at the controller one at a time. If the bike works after disconnecting a brake switch then that switch is faulty and should be replaced.
There is some excellent information on trouble shooting and testing components here http://www.razorama.com/razor-installation-guides.html
also wiring diagrams here http://manuals.monsterscooterparts.com/recreational/Razor/Wiring/

Run time depends on a few things, including the weight of the rider, the terrain being riden over and the condition of the bike.
For example, a light rider riding on flat hard packed dirt or paved road with a bike that is in good mechanical condition - tires inflated to correct pressure, chain correctly adjusted/lubed, brakes adjusted, etc. - will have a longer run time than a heavier rider on soft undulating dirt with a bike that has not been maintained.
Generally you should be able get 40-45 minutes out of a new battery.
Check out the trouble shooting guide and user manual if you are getting less than half and hour.
http://www.razorama.com/ownersmanuals.html

MX350 is a 24V bike.
You could change the gearing by replacing the sprockets, or you could replace the electric controller and upgrade to 36V, but you probably would be better off getting a bigger model, like the MX500, as this uses 36V already and the higher voltage allows for higher motor rpm.

yes .stop playing with the connectors...but that do tell urself that is a future problem

remember the motor transfer the power to the front..there no weight on the motor when you take it off..the motor can be going bad/a singnal! most people change the battery without checking the motor for wear..

Look hard for loose wires. Start with the on off switch. Make sure all are plugged up. The fuse should be accessible without taking things apart. Water is a major enemy of the solid state box the wires go into before they go to the battery.

you could try charging it if this dont work you will have to replace it

i would suggest taking the chain off of the sprocket(cog), then loosening the nuts. then using tire-levers from a bike shop to carefully leve-off the tire. this should work....i have experience with bicycles....i race them! good luck!!!