Via the switch, or directly, can you PING or go online with the L35E controller using RSLogix 5000? Can you PING the PC terminal?
By the way is the process still running today even though the HMI is unavailable? (I notice the fault alarm is time stamped at yesterday's date).
Going by your description, I'm not sure what HMI application you are actually running here, but stripping out the manufacturer references, it's Wonderware, correct?
G.