If the program is not running there will be at least a red indicator (STOP) led flashing or the RUN led (Green) will not be on, so this is a good indication that either there is a fault on the PLC, run switch not in run position or program lost (however, if the program has been lost & a complete restart done then the PLC could be in run mode but unlikely from memory), You will need Step5 software & a 232 to TTY lead to connect to the PLC, this PLC is well beyond it's useful life & spares or software is not generally available from the supplier. The HMI probably was programmed using protool so that software would also be needed. If the program has been lost then without the original source file or at least a copy taken from the PLC it would need to be re-written probably would make sense to upgrade anyway.
This PLC is probably more than 20 odd years old so the backup battery would probably the cause of a lost program unless the program is stored in an eprom (plugged into the front of ther processor) these from memory are orange for eprom & grey/white for ram. To be honest, if you do not have the software & experience to go-online then your only option is to get someone who has the skills to diagnose the problem.