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.