pressure barrels

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I bought 2 barrels with c02 pins but want to try one with normal cap how long will it keep beer fizzy for

As long as you don't drink any. Once you tap it, CO2 comes out of the beer to fill the headspace making the rest of the beer a little flatter. Towards the end, it's really flat. The CO2 connector helps maintain pressure.

For some styles, the low carbonation isn't a problem.

I used to use pressure barrels, and found they were excellent for low carbonated beers like Bitters. The CO2 cartridges kept the carbonation consistent. If you don't use the CO2, as David said, the beer will get flatter, and as you can probably drink faster than the CO2 comes out of solution, you will end up with a partial vacuum in the barrel which will prevent you from drawing off more beer unless you release the vacuum by letting air in. That is like pouring a glass of beer, and then leaving it for several days before drinking it.
As for keeping beer "fizzy", I never tried it, so I don't know how well it would work.

-a.