My White zigzag Model 614 will not turn the hand wheel to take up lever

turn the hand wheel that lever is what pulls the needle thread back up to complete the stitch
it is connected directly to the needle shaft and moves in relation to the needle

Bradford Sewing Machine

If you find the zig-zag lever does not change the stitch width, most likely the machine has seized due to lack of cleaning and oiling.

Wheel on right side that controls the needle up and down is very tight...

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The levers and controls may move but are they activating the internal mechanism? Could be the parts have been seized by old, dry oil.

Wheel on right side that controls the needle up and down is very tight...

If it's a mechanical machine, most likely it needs a good cleaning and oiling.

Wheel on right side that controls the needle up and down is very tight...

Will not zigzag or decorative stitches New to these newer plastic style...

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The lever could be rusted in place; ie. the parts that move across/over each other when the lever tries to move down, don't.

Here is a list of Internet searches for Diagrams; not all of these will be for your exact machine but all are similar. Cast about and you can see how your lever is supposed to work.

Bernina 740 diagram Google Search

Find the pivot point and oil it.

1. The switching pawl (lever on the top cover that switches from zigzag to cam patterns) may be engaged in the cam or automatic pattern side. Check that first.
For zigzag application, the lever must be engaged in the zigzag side (lever pulled back toward the operator). The stitch width dial is then used to provide your choice of width.
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2. It is common, due to oil varnishes, that the switching pawl that is actuated by this lever is stuck between the zigzag and the automatic position, thus preventing the transmission of power to either the zigzag cam or the automatic pattern cams and to the needle.
The best way to detect this is to remove the top cover. You can then switch the lever back and forth to observe if the switching pawl engages firmly into either of the receiving forks. If the switching pawl is sticking, a few drops of certain solvents are applied by a technician on the switching pawl support. The switch lever can be rapidly switched back and forth until you see the switching pawl engage into the receiving forks and you hear a crisp clicking during each engagement. This repair can be permanent or it may create only a temporary fix due to the amount of oil varnishes on the parts.
If the machine is heavily varnished, it suggested that the parts be disassembled and cleaned for flawless performance. If the machine had been sprayed with WD-40, petroleum based solvents like mineral spirits will not break down these varnishes.
A caution regarding solvents...DO NOT USE (WD-40) as your solvent. WD-40 is a marvelous product for its intended application as a water displacement device. It is not to be used for lubricating a sewing machine. Note: "Bernina Technical Information bulletin #1" issued in 1982, forbade the use of such spray lubricants and solvents. SewTechnical Home

We are assuming that the zigzag width dial is at the widest position but the needle will not move laterally for zigzag... The following logic should be applied for Bernina machines 530, 730, 830, 930 machines with a guided motion zigzag cam.
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1. The switching pawl (lever on the top cover that switches from zigzag to cam patterns) may be engaged in the cam or automatic pattern side. Check that first.
For zigzag application, the lever must be engaged in the zigzag side (lever pulled back toward the operator). The stitch width dial is then used to provide your choice of width.
----------------------
2. It is common, due to oil varnishes, that the switching pawl that is actuated by this lever is stuck between the zigzag and the automatic position, thus preventing the transmission of power to either the zigzag cam or the automatic pattern cams and to the needle.
The best way to detect this is to remove the top cover. You can then switch the lever back and forth to observe if the switching pawl engages firmly into either of the receiving forks. If the switching pawl is sticking, a few drops of certain solvents are applied by a technician on the switching pawl support. The switch lever can be rapidly switched back and forth until you see the switching pawl engage into the receiving forks and you hear a crisp clicking during each engagement. This repair can be permanent or it may create only a temporary fix due to the amount of oil varnishes on the parts.
If the machine is heavily varnished, it suggested that the parts be disassembled and cleaned for flawless performance. If the machine had been sprayed with WD-40, petroleum based solvents like mineral spirits will not break down these varnishes.
A caution regarding solvents...DO NOT USE (WD-40) as your solvent. WD-40 is a marvelous product for its intended application as a water displacement device. It is not to be used for lubricating a sewing machine. Note: "Bernina Technical Information bulletin #1" issued in 1982, forbade the use of such spray lubricants and solvents. SewTechnical Home

If you can grab the hand wheel and move it right and left, then it probably needs a plastic collar that goes next to the left upper shaft bushing.
If not then the cam timing needs to be adjusted.