Another DBA accidentally launched a batch (.bat) file which rebooted the server, which resolved the issue. However, the link was working fine. I stopped and started the DTS services and it did not correct the problem. In all of my research, it appeared the hung/orphaned processes were not doing anything. It appeared as if the master..sysprocesses table was not cleaned up properly until the reboot.
I was hoping to resolve this without a reboot but now I'll have to wait for it to occur again.
I will still take an answer if anyone has one.
Thank you.