Try using something smaller than your finger to press the open key (button). A smaller object may help to press the key all the way in. Also try pressing the key closer to the left end & closer to the right end, instead of the middle of the key.
Sounds like the connection between the blades & the motor is worn. Separate the driven blades part from the driving motor part. Look at both the driving & the driven parts of that connection for wear & breakage. If there are broken/missing/severely worn parts of either connection, replace them. You may have to get a whole new section with the motor or a whole new section with the blades, if not both. If they both need replacement, just get another Cuisinart.
Don't know about ruined screw head removal, but for future reference: Place the tool lightly on screw head & rotate axially 'til the tool drops into the screw head for a comfortable, firm fit, before applying pressure & torque for screw removal. If the tool does not drop in the screw head for the comfortable, snug fit, you may have the wrong tool or the wrong size. Try a different size 'til U get the right fit before applying pressure & torque to remove the screw. It can save you grief from a ruined screw head.
Better leave the back pack where it cannot fall. Hindsight is so much better than foresight . I learned the hard way too!
Don't know about ruined screw head removal, but for future reference: Place the tool lightly on screw head & rotate axially 'til the tool drops into the screw head for a comfortable, firm fit, before applying pressure & torque for screw removal. If the tool does not drop in the screw head for the comfortable, snug fit, you may have the wrong tool or the wrong size. Try a different size 'til U get the right fit before applying pressure & torque to remove the screw. It can save you grief from a ruined screw head.