From your SM50 screenshot we can see that your only one update dialogue work process is hanging, and I suppose that's the root cause.
Find out why it is hanging.
For are start check SM13. Is update active?
Then check database logs for problems. Something like tablespace full in case of Oracle, for example.
If needed ask your Basis team for help again.
Then you might consider to increase the number of update work processes.
hope this helps