If the two hots read 0 volts there is no potential, therefore no current will flow when needed and the welder will not work.
If you hook up an occilliscope (sp?) to a 120 volt outlet, you will observe the 'wave' curving up above the zero volt line and then curving down below the zero volt line. For simplicity's sake, when the curve is at it's highest peak, you would see 120 volts positive. At the lowest point, you would see 120 volts negative. This changes 60 times per second, hence 60 hz frequency. Lets call this leg L1.
L2 does just the opposite of L1. When L1 is going up above the zero volt line, L2 is going down below the zero volt line. These two swap positions 60 times per second. If you measure the voltage between the upper peak of L1 (+120 volts) and the lower valley of L2 (-120 volts) there is an ABSOLUTE difference of 240 volts.
L1 and L2 will both read 120 volts to ground, because ground is the zero line on the scope. If you measure between L1 and L2 correctly connected, since they are 180 degrees out of phase, they should read 240 volts.
To get 240 volts from your panel box, the breakers that have the handles tied together for 240 volt each get power from a different leg of phase, that is, L1 and L2. DO NOT ATTEMPT TO GET 240 VOLTS FROM ANYTHING BUT PROPERLY CONNECTED BREAKERS WITH THE HANDLES TIED TOGETHER FROM THE FACTORY. THIS IS CRITICALLY IMPORTANT!!!!!!!!!!!
If one leg of phase developes a short circuit, that breaker will trip and will also trip the other leg of phase so that the entire power circuit will be dead. If you had two separate breakers and were lucky enough to have them feeding on different phases, the welder would work. However, if one leg of phase tripped, the other leg might not. YOU COULD GET ELECTROCUTED ATTEMPTING TO TROUBLESHOOT THE PROBLEM BECAUSE UNLESS YOU PHYSICALLY MADE SURE BOTH BREAKERS WERE OFF, THE OTHER LEG OF PHASE WOULD BE DELIVERING POWER LIKE NOTHING WAS WRONG.
I am in agreement with leitmotif, you need to get a sparky (electician) in there to make sure things are correct.
