Veritas cluster issue

If this is VxFS filesystem, add '-F' vxfs to the mount command.

Maybe best to fsck filesystem first: 

fsck -F vxfs /dev/vx/rdsk/bgw1dg/vol01 

Then mount it:

 mount -F vxfs /dev/vx/dsk/bgw1dg/vol01 /var/opt/BGw/Server1

The reason why diskgroup 'disappeared' after reboot is because it is under cluster control and imported with '-t'. 

PS: Not sure how you hoped for a reboot to fix the 100% full issue? 
Seems your Service Group is not configured to automatically failover to 2nd node when system is rebooted?

As this is 100% full..that is why????

As everyone above has pointed out, the filesystem being 100% full is not going to cause the fs to unmount or the dg to deport in and of itself.

If the dg and filesystem are clustered, and an application depends on them couldn't write to the filesystem due to it being full, if this would be enough to fault the application, this could have triggered a failover if the application was configured as Critical - so VCS would have taken the group (including the filesystem and dg) offline and brought them up elsewhere if it was able.

However, this is only one possible scenario based on many many assumptions - you need to look at your configuration and logs to determine exactly what happened in your case.