Kegging Pressure - Naturally Carb

I am very new to kegging. In fact, my experience is limited to this keg for which I have questions. These are the steps I followed:

1. Naturally carbed my Simple Hefeweizen with 2.5oz corn sugar (mixed into a simple syrup and mixed in my bottling bucket prior to transferring to the keg.
2. Used the 12g hand CO2 dispenser on my ball-lock to ensure a properly sealed keg
3. Waited 3 weeks in my 68F basement.
4. Attached my short picnic tap (about 1').
5. Served test sample at 68F.

It comes out all foam. It settles back to beer, but naturally without any carbonation. How do I fix this? Do I bleed pressure off using my pressure relief valve? If so, how much? Do I chill it down to serving temp and hope that the CO2 goes into solution better?

Please assist a fledgling kegger!

Caveat: I have no keg fridge/keezer or anything right now, I would have to either wait for an opportunity to buy one or chill the keg in an ice bath and drink all 5 gallons in one sitting (not a horrible option, just makes for a hell of a hangover...).

Well, I hate to break it to you...but, you are going to need to chill that keg or make a jockey box.

First thing I would do is check to make certain there is pressure (Pull the relief slightly), (Hopefully you leak checked it after you filled it?) then I would lay that sucker on it's side and thrash it around for a while to make certain the CO2 is absorbed, do it again the next day or just every time you walk by or think about it. Then I would try a longer tap hose for one, like 6' to 10'. The entire problem may be that it's still warm? You could also just pull the relief until pressure is manageable, then pour one, your natural carb action should maintain enough pressure to dispense, like a cask ale. I naturally carb my kegs all the time but have never served one at room temp.

You could rig a simple jockey box if you have more tubing, otherwise it would take a long time and alot of ice to cool a keg without a fridge, speaking of the fridge, just throw out all the unneccessary stuff from your fridge, like food, milk, etc and put the keg in there. You're still gonna need a longer hose though.

That keg's going to have to be cold for the C02 produced by fermentation carbonation to dissolve into the liquid. When I do a keg this way I let it sit at room temperature for a couple of weeks, then chill it down for a day or two, then tap it and drink. Little to no foam, nice carbonation.

Thanks everybody for the quick feedback. I guess I am going to have to convince SWMBO to let me buy my chest freezer and temp control early!

You didn't say that you attached CO2 pressure to serve the beer. If carbonated, some will come out but you'll need constant pressure to serve the whole tank.

Btw, I'm a step behind you. I'm about to try kegging for the first time this weekend and I'm trying to decide if I should naturally carb while I order keezer parts at reasonable prices online, or support my LHBS and pay 30% more so I can force carb now.

Edit: I see that you wrote this over a month ago. How did it turn out?

Sorry to revive/hijack an old topic.
I am doing my first batch and will be carbing my beer through natural pressure. I need to upgrade the keg to one fitted with a co2 vent cap, and I don't have a keg fridge.

I couldn't see a natural carbing sticky, and have scoured the internet but couldn't find the answer to the following questions. (It seems most posts are about co2 carbing).
1. How much sugar will I need to prime the keg? (Coopers English Bitter + 500g light spray malt)
2. How can i improve the pressure in the keg aside from putting vaseline on the seal?
3. Any tips on how to improve the carb of the beer through natural pressure during any part of the process?
4. Without a fridge how can I combat any problems?

Many thanks!