When I depress the carriage control levers they do

I woulsd suggest just exchanging it at BBB. Their retun policy is very liberal.

I repaired the same symtom that happend to one of the sides of my CPT-180 toaster. The magnets wouldn't engage due to a bad C1 capacitor on the circuit board that controlled that side of the toaster--the capacitor was bulged out on the bottom and turned out to be bad. I've attached some photos showing C1 bulged out compared to C1 on the good board.
C1 is the main power supply capacitor and if it goes bad, the circuit board power supply won't function correctly. This can lead to a broad spectrum of problems like the lever not staying down due to the magnets not engaging or the toasting control/timing circuits malfunctioning. If you replace the capacitor, it is best in most cases to replace with the same value as the orginal (220uf on my toaster)---you can usually get a replacement capacitor at Fry's Electronics. Replacing with a higher capacitance may be acceptable, but you should understand the impact to the rest of the circuit before you substitute a higher capacitance value. The voltage rating and temperature rating of the replacement capacitor should be the same or greater or the capacitor will fail quickly. Note the max temperature rating of capacitor C1 is +105C---toasters get hot (duh!) and the temperature around the circuit board of this model gets quite warm, so the temperature rating of the capacitor is critical. Finally, make sure the substitute capacitor fits when installed (requires soldering) and does not interfere with surrounding circuitry or other toaster mechanics when the circuit board is put back in place.
Pictures:
C1_location (next to screw)
Comparing_good_C1_with_bad_C1--note bulge on bottom of right C1
Right_orginal_C1_and_left_replacement_C1
Bad_C1 showing capacitance, voltage and max temperature ratings

I repaired a problem with one of the sides of my CPT-180 toaster that was fixed by replacing C1. This may be the same component that Stan was referring to, as the C1 capacitor on the circuit board I was having problems with was bulging. I've attached some photos showing C1 bulged out compared to C1 on the good board.
C1 is the main power supply capacitor and if it goes bad, the circuit board power supply won't function correctly. This can lead to a broad spectrum of problems like the lever not staying down or the toasting control/timing circuits malfunctioning. If you replace the capacitor, it is best in most cases to replace with the same value as the orginal (220uf on my toaster)---you can usually get a replacement capacitor at Fry's Electronics. Replacing with a higher capacitance may be acceptable, but you should understand the impact to the rest of the circuit before you substitute a higher capacitance value. The voltage rating and temperature rating of the replacement capacitor should be the same or greater or the capacitor will fail quickly. Note the max temperature rating of capacitor C1 is +105C---toasters get hot (duh!) and the temperature around the circuit board of this model gets quite warm, so the temperature rating of the capacitor is critical. Finally, make sure the substitute capacitor fits when installed (requires soldering) and does not interfere with surrounding circuitry or other toaster mechanics when the circuit board is put back in place.
Pictures:
C1_location (next to screw)
Comparing_good_C1_with_bad_C1--note bulge on bottom of right C1
Right_orginal_C1_and_left_replacement_C1
Bad_C1 showing capacitance, voltage and max temperature ratings

The Instruction Booklet for the Cuisinart CPT-180C Classic Metal 4-Slice Toaster can be found at the following link:

http://www.cuisinart.ca/pdf/ibs/en/CPT-180C_en.pdf

Not sure what you are trying to open. There is a slide out catch tray for cleaning crumbs. There is no information in the booklet that suggests a need or a way to open the toaster.

Perhpas reviewing the booklet will answer your question.

wrapped a rubber band around it, attached vise grips, and pulled very hard.

for Cuisinart cpt160: If the latch will not stay down it is because the electromagnet at the base of the toaster, which is supposed to activate when you push the handle down, is burnt out. I pulled my toaster apart and did a test of that mechanism and found that the solenoid was fried (open circuit). There are no replacement parts.

First, turn it to the darkest setting. It may be set too light to stay down. Also, try cleaning it out. Take it outside and turn it upside down and shake it. Also, open the crumb door on the bottom. Hope this helps. Good Luck.

Do any of the lights come on ?

If not then have you checked the plug top fuse

If the lights come on and then when you press the lever down it does not latch a solenoid has gone open circuit

Good toasters can be fixed

Cheap ones go in the trash bin

Arms stay down by the mean of an electromagnet, controlled by a chip. If the wall outlet is functional, you should be able to turn on light by pressing the "defrost" or "bagel" button while the arm is held down. No light? the toaster is good for garbage!!