Sounds like your Interactive subsystem is not started.
Sign on at the system console.
do WRKACTJOB to see what is going on.
you should be able to STRSBS QINTER (or whatever subsystem you use), then you will be able to use your other devices.
How did you set off your backup manually? Are you using the GO SAVE options, the GO BACKUP menu or a in house save program?
If you are submitting it manually, you should verify what else the backup does, in this case it appears to end QINTER and restart when complete. It may be shutting down other services that may have to be restarted as well or calls your QSTRUPPGM program.