These come in many different size "bundles", so I was unsure how many you had.
This is most likely an internal hardware failure, meaning the lcd display screen has failed.
A bad battery would not produce that symptom. If the battery were that low/faulty, then you would not be able to make/receive calls either.
This is a very old system (2 generations of technology ago, replaced by the 5.8ghz then the dect6 systems), so seeing this type of failure just from normal age related wear and tear is not surprising.
You can reset the handset by removing the battery from it for 15 minutes.
If no change, then the handset is defective, and would have to be replaced. Unfortunately, there are no parts for these systems any longer, so you'd need to replace the entire system (base + handset), which would be more feasible than either parts or repairs.
Here is a replacement I'd suggest:
Best regards, ***** ***** for the news,