No worries about being offline.
If you haven't already tried NEW rechargeable batteries (fully charged) in this one handset, OR swapping the batteries with the WORKING handset, that is the first thing I would try.
BUT, if the display is ON, but no letters or icons are showing (like the working handset), then the display or circuits that drive it may have failed.
Since this system is past its 1-year warranty period, I suspect it would cost much more to repair this handset than to replace it - with a "used" handset of the same type.
I have a link below to an Amazon listing, where there are NEW and USED handsets of this type listed. You may want to take a look at both and see what suits you best.
Click here --> http://amzn.to/2cRn8Rw
NOTE: Once you have the handset, it will need to be "registered" to the base unit, so that it will operate properly. If you need help with that, let me know the model of the MAIN BASE of the system, and I can give you those steps.
Please let me know what you find with the battery change/swap, or if you have any more questions.
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Thanks, ***** *****