Sewing machine needle is stuck and the machine will not move.

Try ironing the hem in place first and then loosen the bottom plate tension. Does sound like a tension issue though

probably sewing through the heavy jeans pushed the needle up to far. Loosen the screw that holds the needle and lower it down a little

You need a couple of things. One is to flatten the seams before you try to sew them. One of the best is to spread the hems on a wooden cutting board or simiilar smooth surface and beat the hems flat with a flat faced hammer. This is an official sewing hammer: http://www.fashion-incubator.com/archive/tools_and_supplies/ and it will compress the fabric so it doesn't lift your presser foot up and let the tension off the top thread (which is what's causing your looping problem).

For crossing thick seams, you need a shim to keep the presser foot flat while sewing. These are usually called hump jumpers or jean-a-majigs, and are a couple of bucks. Or you can use a fold of fabric in the same way: http://www.youtube.com/watch?v=WbYenXIDaDk http://www.youtube.com/watch?v=ZKdW_vIZLBo

Alternatively, you can do the jeans hem alteration that pros will charge you more for (because it's "fashionable"), and it's also faster and easier. Often called Euro-hemming: http://www.sewmuchado.com/2011/06/tutorial-how-to-hem-jeans-and-keep-the-original-hem.html

Sounds a bit serious, jeans fabric is dense and thick. Many machines struggle especially sewing hem over side seam with 6+ layers. You need jeans needle size 90, 100 or 110. Maybe take in for a service as the needle assembly could be out if time too

Are you trying to use a heavy thread like buttonhole twist through the needle like the yellow thread on store bought jeans? Most domestic machines will not cope with this heavy thread and it will be too large for the eye of the needle too.

If you are using regular weight 50 polyester thread and its breaking then it could be because the top tension is too tight. Just loosen off 1/2 a number on top tension dial and see if this helps.

If possible, buy a pack of jeans needles size 100 too, these are blue coated with teflon I think, and makes it easier to slip through denim which is a very dense fabric.

Hemming denim jeans is probably one of the toughest jobs for a domestic sewing machine so if you are trying to do this, its a good idea to take it slowly and use a "humpjumper" which helps to maneouvre over the thick side seams.

However, even with all the above, many machines won't sew more than one layer of heavy dense weave denim.

If you think its the way the material is being moved, I would check the pressure on the presser foot. On my machine, there a knob with 1,2,3 to adjust, its vertically above the foot on the top of the machine(Check you manual). Sometimes the jeans hem is just too thick on the side seam. I just skip that part, or move the needle through that part by using my hand on the wheel, so the stitsches look ok, but it should do the rest of the hem fine. Try the thinnest part of the hem first; good luck

iam reliable informed that you will need to change the needle by the one who controls this machine in our house for different thickness materials you need different size needles ,or you will get exactly the problems you describe ,iam told to look in the book and see whats suggested for this sort of material ,as some of the smaller machines will not go through tougher type materials and some jean material you will have to do it by hand with a special long needle ,the type of needle i use on my boat for the awnings and sail .

try a
Jean-a-ma-jig or Hump-jumper
trying to sew over a bump of fabric, such as a thick jean hem, try using this tool
local fabric store should carry it
It keeps your pressure foot level as you sew over the
bump
you said your needle plate has many strike marks on it,,make sure you can't feel the strike marks so the fabric won't hang on them,,because marks on a needle plate can pulled the fabric

I turned up my husband's jeans using a size 100 needle. You can get easy thread needles that have a small gap in one side that you slide the thread through. There is a good way to turn up jeans and keep the original hem without having to cut them. Have a look at this site http://www.daciaray.com/?p=38

Are you using the correct type of needle? have a word with your needle supplier and explain the problem. Different threads and different thickness material need different top and bottom tension adjustments.
Can I suggest sew one thickness material at a time with tension adjustments for that thickness. Then change the tensions and do a batch of thicker material.