In theory, USB 2.0 ports are only capable of supplying up to 500mA to external devices.For USB 3.0 ports it's 900mA. This is not a hard and fast rule.
A Y-cable connected to two USB 2.0 ports should be capable of supplying 1000mA (2x500mA) which is only 100mA more than USB 3.0.
If the drive used to work on a single USB 2.0 port, lack of current is not the problem.
The WD3200BEVT is a 2.5in hard disk. These drives were often fitted in laptops and usually work fine on a single 5V 500mA USB 2.0 port.
Your old hard disk case might have used a direct SATA to USB translation bridge chip. The new case might use a SATA to USB bridge chip with "sector translation".
https://goughlui.com/2013/10/02/experiment-usb-to-sata-bridge-chips-and-2tb-drives/
Try connecting the WD3200BEVT directly to the SATA port in a desktop PC. If the hard disk works OK in the desktop and you can view files on the drive, the hard disk is operating without sector translation.
It's possible your new case is not compatible with your old drive.
N.B. Sector translation was invented when hard disk capacities crossed the 2TB barrier some years ago.