You're not a lost cause, to me there are a few problems that should be easily fixed.
Right there are 2 types of back squat. The high bar squat (olympic), and the low bar squat (powerlifting). I won't go in to all the differences as it will just got confusing. We'll just go through how I squat. By all means look at the other styles as they may suit you better.
First of all is your set up. I have a bit of a ritual I complete before each set, I do this as i know it helps me get in focus and be set up right. You might not do this, it's up to you.
Right set the bar lower than you have been probably by one notch on the rack, and set the safety bars a hell of a lot lower. If there at waist height you aren't really squatting. When you squat the crease of your hip want to be at least parallel with the crease of your knee.
Now grab the bar with what you feel will be as narrow grip as you can and still remain comfortable. Then step forward under the bar with both feet (ditch the towel). I have my feet slightly wider than shoulder width, my toes at about 35 degrees. Now push your shoulder blades together as hard as you can, as if your were going to trap a pencil between them. I position the bar on top of my rear deltoids (low bar), the other option is your upper traps (high bar). Keep this position, shoulders pinned, chest up arse out so the bottom of your back arches. Now pick a point in front of you at eye level a fix upon this. Take a deep breath in and lift the bar out of the rack like you mean it, then exhale. Now take one step back with your left leg, and one with your right keeping the earlier position, and eyes focused on the point in front of you.
Now you want to push your feet out to the side as if you were trying to split the floor beneath you. Take a deep breath in, hold. Then arse back first, as you drop keep pushing your feet and your knees out to the side. Keep your sight fixed. When you hit parallel drive your elbow under the bar and drive up with your legs - keep pushing them feet and knees out. Once you reach the top exhale. And repeat for the next rep. Make sure you keep your head up and sight fixed as this should prevent you from going on to for toes. If your having trouble with depth try doing some box squats or put a large medicine ball underneath you.
Hope this helps and I've managed to explain it so you understand it. it's automatic to me so getting it down on paper for someone to follow was harder than I thought. Give it a go, and let me know how you get on. If you've any questions just ask, and if you don't understand what i've put I'll point you in the direction of some clearer explanations.
Other things to consider are what footwear you have on while squatting. Your choices are converse chucks, lifting shoes, or a specific squat shoe. If it's none of these go barefoot. Things like really minimal footwear such as new balance minimus, inov8 bare xf's will also be fine but not as good as the above 3. I wear Adidas power perfect 2's. Prior to this it was minimus then barefoot as things got heavier.
Warm up and stretching is also very important with squats. Lots of roller work on itb and piriformis will do wonders. At least 30 reps each side. Also stretch your hamstrings using a band if you have one available and do numerous sets of air squats concentrating on depth and form.
The warm up sets: Do 2x5 with an empty bar, 1x5 bit heavier, 1x3 heavier still and then 1x2 heavier still. Following this should be you work sets. I imagine your doing three sets of 10 at the minute. Try changing this to 5 sets of 5 and see how you get on.
One last thing if you're struggling with depth and form reduce the weight and concentrate on getting things right and increase very slowly, no more than 2.5kg at a time.
Hope this helps and I've managed to explain it so you understand it. it's automatic to me so getting it down on paper for someone to follow was harder than I thought. Give it a go, and let me know how you get on. If you've any questions just ask, and if you don't understand what i've put I'll point you in the direction of some clearer explanations.
Happy squatting.