Setting aside if Carthage truly could have conquered Rome properly - I'm with Brian in this one, in that there were a lot of factors that essentially ensured Carthage was going to lose no matter what - there is a problem speculating what a victorious Carthage, if there had been one, would have done.
This is because Rome eventually stamped out brutally the Carthaginian civilisation and very effectively Romanised all of it's people. Hence there are very few primary sources of what was going on in the Carthaginian side - every contemporary source comes from outside, as far as I am aware (and usually from the Romans themselves - example: the claims of child sacrifice in Carthaginian society/religion is IMO quite suspect.) Would it have spurred them onto a Rome-like empire or would they have been content to control the Italian states loosely, deal with and allow a strong gaul/celtic North and focus on getting rich on trade? Or something else.
I think any outcome we come out with will seems as likely as another, give our lack of knowledge.
One thought though - if there had never existed a strong Empire that was stable for hundreds and hundreds of years and stretched from the moors of Northern England to the Sahara, the Atlantic ocean to the banks of the Euphrates, essentially allowing the transport of trade, people and ideas...would that fledgling religion Christianity have had the opportunity to spread beyond the middle East? I believe it wouldn't have - Christianity became successful when it converted, bit by bit the Roman civilisation. I think it would have a had a much harder time converting a hodge-podge of states (if that's the scenario we have
)