Besides the meter base, check the main panel. The short may have burnt out the connection to one side of the main panel or the bar itself under the stove breaker. 240 volt circuits derives it power from both sides on the main power bars. The 240 volt breakers sit above the others. Turning on the dryer may put power from one side through the dryer over to the other (hence turning on your other lights) but you may only be getting 120 to the dryer which wouldn't allow the element to heat up right.
Check this out and post back. Remove the stove breaker to take a look. You will need an electrician to fix this and it won't be cheap as you may need a replacement bar or a new panel. Good luck.