Did you get your machine working again? I've had trouble with the feed dogs when the thread has gotten gnarled up under the needle plate.
Some machines do have a knob or wheel to adjust the presser foot pressure. Check your manual if you have one, or post your machine model here and maybe someone has one like it.
It can be hard to start seams in thick layers of fabric. I like to make a thread handle with the ends of the needle and bobbin threads to pull on gently to help start the fabric feeding. Before you put your fabric under the the presser foot, pull the bobbin thread to the back of the presser foot. Make sure the needle thread also runs under the presser foot and put it in the back with the bobbin thread. Place your fabric layers under the foot, lower the presser foot, start to sew. After the first two or so stitches into the fabric, gently pull on the threads behind the presser foot. Once your machine gets going, you should be fine. If not, maybe four layers IS too much for your machine. Maybe you can redesign the pattern to use fewer layers at a time.
Caution, don't pull too hard or you can mess up the timing on the machine. Just a tug to help the machine feed more easily is all that you should need. Putting the threads neatly to the rear of the needle is a good habit anyway, it helps to prevent those thread snarls on the bottom of your seam.
HTH, I hope you figured out your problem!
