No bubbling in the air lock for more than 4 days

I bought a starter "pail" kit and made my first brew on Sunday. I followed directions, sealed the pail, added the air lock with a shot of vodka. It is sealed well. I've watched you tube videos and I have seen that sometimes fermenting takes over 24 hrs. Now it's about 4 days. I removed the air lock and I do see a foam and a lil built up gunk around the sides. If I follow directions I'm supposed to bottle in 3 days , but should i??.. I've kept it in a room that has stayed 19 degrees. I know it's a little cold.. Anyways please help. Is my brew screwed?? Should I toss it and start over?? Thanks

There is nothing wrong with your beer. Be patient wait at least 2-3 weeks (from when you first pitched yeast) to let the yeast clean up (the longer the better) before you bottle. 19C would actually be a fine temp for an ale. If you want to help speed up the process a little, go ahead and move it to a warmer place if possible.

The active fermentation where sugars are converted to alcohol, ending in a final gravity can sometimes only take 48 or so hours, but often takes longer than that. The remaining time is to let the yeast cleanup all the byproducts they made. If you bottle now, the beer might taste "young" or "green". Give it time to bulk condition on the primary yeast.

Sounds like you've had fermentation. Did you take OG? Even if not, take a FG reading in a couple days, then take another 2-3 days later. If it is constant, it is safe to bottle. Most people will tell you that in general, you should wait about 3 weeks in the primary, regardless of what the directions say.

Just because there are no bubbles doesn't mean that it is not fermenting. The only way to be sure is to take a hydrometer reading to see if the gravity is less than when you pitched the yeast.

If there is foam and "gunk" on the sides it is probably working.

A bubbling airlock is not an indication of fermentation. You may have a leak or did not seal the pail good enough causing the CO2 to escape through easier openings. The only way to determine if your batch has fermented is to take a hydrometer reading. Did you take a starting gravity reading to know where you started and where it is now? The gunk you mentioned is Kraeusen, which is the foam created by fermentation. Your brew doesn't sound screwed and I would leave it in the primary "pail" for at least 2-3 weeks to finish fermenting. Learn to throw out the instruction a kit comes with and go to howtobrew.com to get a better idea of what to do. Bottle when you get 3 identical gravity readings over 3 or 4 days and when it is within the specified final gravity that the recipe calls for. Do not throw it out, see it all the way to the end.