Carbonate beer in a plastic keg

My guess is that those CO2 bulbs are designed to fill the vacuum formed by pouring beer, just like the CO2 you hook to a keg you're tapping. All it does is prevent your beer from being introduced to oxygen. Take a look at this site for some pretty good instructions on carbing your beer.

I doubt you'll be able to carbonate the beer without significant quantities of those. However, once the beer is carbonated, the bulbs may be enough to maintain pressure while dispensing -- which I think is closer to the intended purpose of this setup.

My advice? Add 1 cup of dissolved priming sugar, wait a week, and give it another try.

It's hard for me to imagine that you can build up sufficient pressure in a plastic keg to carbonate with just static pressure - it's going to take a while to get the CO2 to be absorbed by the beer. I don't suppose there's any way to get a pressure gauge in line with this rig? If you go by this chart, you'll see that at 5-10 degrees C (41-50 degrees F), you'll need almost 15 PSI of CO2 (assuming you want about 1.9 - 2.2 volumes of CO2 dissolved - standardish for ales).

If you're using a 5 gallon pail, that has about 113 square inches of area, so the force on the lid would be very nearly 1700 pounds. The good news is that there's no way it's not going to leak, otherwise the possibility of explosive failure is pretty good.

On the other hand, if you're using a more typical soda pressure vessel, then you're all set - you probably just need to add more pressure to the rig to get carbonation.