Just drank 10 raw eggs.
Don't be discouraged. You just have to take things one step at a time.
The fact that you can't touch your toes or do squat holds is irrelevant; I can't touch my toes for the life of me and I can squat just fine. In fact when I started squatting I was the least flexible person I knew.
The most important issue when people are unable to squat to depth is foot positioning. Unless you have good ankle flexibility, you won't be able to squat with your toes pointed forward. Most people have this idea of the squat with toes pointed forward and a very narrow stance, but that is unrealistic and also not very conductive to great squat mechanics.
Since you lack flexibility you'll have to point your toes outwards, about 30°. And you want your knees to track your toes as you squat down. Because your feet point outwards, you'll have to shove your knees out for them to track your toes. And this accomplishes two things: first, it will get your femurs out of the way so that going deep is easier. Secondly, it'll force you to engage your adductors (the groin muscles) more thoroughly in the squat, because the adductors are what prevents your knees from caving inwards.
The other adjustment you'll have to do is to widen your foot stance. For most people, shoulder width is enough, but you might want to try going a bit wider.
So, toes pointed outward, shoulder wide-foot stance (or a bit wider) and shove your knees out. To practice these cues you should start without the bar. This is a recommended stretch that will also help you ingrain what the bottom of the squat feels like:
*
Try to hold that for a few seconds. Use your elbows in the position shown in the photo to help shove your knees out so that they track your toes.
Then use the empty bar and do 3 sets of 5 reps, following the same cues, and take it from there, adding 10lb per workout until they start to feel heavy, and then add 5lb each workout. Be conservative when adding weight to the bar, but if you do it correctly you should be able to hit proper depth while also increasing your flexibility with each workout. Of course, there's more to the squat than that, and if you are really interested in learning the lifts, then you should buy
Starting Strength. The Kindle edition is just $10.
And stay the hell away from the smith machine. The only things you should ever use a smith machine for are leaning over while resting between sets and hanging your jacket.
*Taken from Starting Strength: BBT 2nd Edition, p13.