Thank you for your question as to why the needle will not pick up the lower thread.
These are very good sewing machines. My wife and I have a number of them and they are great since we do a lot of sewing with quilting.
All I think you need is a minor timing adjustment.
But first make sure you have the needle installed correctly with the flat side of the needle to the back of the needle holder. This is all it would take to prevent the shuttle hook from picking up the needle thread.
Since you have already done so many things to fix the problem I am going to go directly to the timing of the needle to the shuttle hook.
As the needle goes up and down the very point of the rotary shuttle hook has to be right behind the needle as to pick the thread.
So this is what I would like for you to do to see if the machine is out of time.
Remove the needle plate cover and the needle plate and remove the shuttle case and the bobbin.
Set the machine to a straight stitch setting.
Turn the machine over very slowly by hand and bring the needle down to the bottom of it’s stoke and stop at the very bottom. Now bring up the needle only about 3/16 to a 1/4 of an inch off the bottom and stop.
The very point of the shuttle hook should be right behind and slightly above the eye of the needle.
If it is not there it will need to be retimed.
To do this you will need to remove the bottom of the free arm cover to get to the Allen set screws on the shuttle drive shaft on the under side of the shuttle.
It looks like with this size case on this sewing machine you will need to get the front face cover off before you can get to the shuttle area.
This may be a little more of a problem for you.
The picture below will show you the locations for the Allen set screws to loosen to hold the hand wheel an turn the shuttle hook so it will line up as I described above.
Do not pay attention to the verbiage because you do not have the timing device but you can do it with out the tool the technicians use.
If you do not feel confident repairing this problem yourself, then you can have it repaired by a Sears technician. Here is a link that will provide the nearest drop-off locations:
Sears Home Services
Please let me know what you have found and if you need more help to retime this sewing machine.