DC motor won't spin with PWM unless touched with hand, and other hand touches "ground" from metallic cabinet
First you'd draw a schematic and ensure the 0V between the Uno and the L298 board is connected. You'd then be able to post the schematic where others could look at it.
As for the 'tingle' - how is this powered? By a switchmode supply from the mains?
Assuming you have a valid schematic, you'd then visually check your wiring. Then if there is doubt, use the multimeter to make measurements at various nodes. Measure where? you might ask. That's where a schematic helps us to help you, otherwise we're just waving our hands around some nebulous device.
Your problem is unlikely to be due to the DC motor - more likely a wiring issue.