If I read your description correctly it says the DRO counts in the direction you command but the Y motor moves in a random direction. This could be a fault on the BOB board.
Try swapping the A axis pins with the Y axis. Change the MACH3 configuration page and move the wires from P2 and P3 to P8 and P9.

Made the changes as you suggested but as applied to the Y axis. Moved wires from P4 and P5 to P8 and 9, and reconfigured the pins in 'Motor Outputs for the Y and A axes. The Y channel still changes the Y motor direction at random.

Changed the Y Pul (P4) and Dir (P5) connections to the X and Z channels and random direction change of the Y Motor continues.

It would have to be a Mach3 setting or the computer , wouldn't it?

I checked all the soldered joints again ... all OK.

I also checked the Mach3 settings as per the BOB installation guide ... but the Device Manager/Mach X Pulsing Engines/Mach3 Driver computer icon has a Blue question mark. The ECG Savebase BOB User Manual states that the ? should not be there. Could this be the issue and how do I remove it?

Changed the Y Pul (P4) and Dir (P5) connections to the X and Z channels and random direction change of the Y Motor continues.

I 'm not sure I understand what you meant here.

Did you try assigning X or Z axes to pins P4 and P5 to show that hardware works?

It does sounds like you have eliminated the BOB as the source of the problem.
If you don't get help from a experience MACH3 user here you might want to start a new topic.
If there is no other alternative you could uninstall MACH3 and start again.

That's correct, I assigned the other axes P2, P3 and P6, P7 connections and Mach3 Motor Output pins to the Y motor but the problem persists, so yes, it would have to be the Mach3 setup or the computer itself.

Before I start a new topic re BOB and driver setup in Mach3, I'll reinstall Mach3 to see if the Mach3 Driver installs without a question mark.