The ornamental design for a ballotboxstorage and transport cart, as shown and described.
FIG. 1 is a perspective view of a ballot box storage and transport cart showing our new design;
FIG. 2 is a front view thereof;
FIG. 3 is a rear view thereof;
FIG. 4 is a left side view thereof;
FIG. 5 is a right side view thereof;
FIG. 6 is a top view thereof;
FIG. 7 is a bottom view thereof; and,
FIG. 8 is a front view thereof, shown with the shelves folded.
The broken line showing of voting equipment and mounting brackets is included for the purpose of illustrating environment and forms no part of the claimed design.