My home central AC system was not working and I tracked the problem to the transformer. I measured the voltage across the transformer and there was 120 volts on one side and 0 volts on the other which showed it was bad. So, I replaced the transformer and the AC started working. However, it only worked for about 1 week. I checked the transformer and there was no voltage as before. Why would the transformer keep blowing out? The original part number was C6349701 and I replaced it with C6349703. Is this correct? Could the transformer have been bad? We have been having bad weather. Could a power surge damage the transformer?

Most Central ACs I see use 240 volt transformers, I will see what I can find with those numbers,
From what I usually see is if you measure for continuity on the primary side and it is open, It may be Primary voltage problem, If secondary opened, you may have a short, on thermostat, control wiring or shorted windings on a relay or contactor.

Looks Like the 701, 702, and 703, is basically the same:
C6349701 Transformer (http://www.allpartsheating.com/c6349701.html)
It says all 3 are 120 volt primary.