Not all fermenting buckets are air-tight, which means that occationaly you'll have a bucket where the airlock on top does not bubble properly. This by itself is not a problem. Also, your mistake with the corn sugar won't really hurt you, and it is not the reason you have no bubbles.
What you need to do now is take off the lid of the bucket and see if you've had any fermentation. Signs of fermentation include, but are not limited to:
- Scummy looking foam on the top of the liquid.
- A brown ring above the line of the liquid
- Floating yeast clumps on top
- The presence of C02 in the head space of the bucket (you can smell this, it's a "sharp" sort of smell)
If you don't see any of these things, the best thing for you to do is to buy a hydrometer from the store and a new packet of yeast TODAY and go take a sample from the beer. If the hydro sample is at or near to the starting gravity of the beer (which should be on the kit instructions) then fermentation has not begun and you need to add the new packet of yeast.
If the hydro sample is significantly* lower than the starting gravity, or if you see the signs in the list above, then you are fine. Just seal the lid back up and leave it alone for 3 weeks before doing anything else.
* Edit: By "significantly", I mean something like .02 points lower or more. So 1.045 is not "significantly" lower than 1.050, but 1.030 is.