This unfortunately points to a defective base station.
or the wiring in your home) OR a hardware failure in the base station (since the issue happens with all handsets). We most often see this type of damage to the base unit as the result of a power surge, either through the phone or power lines. This would be consistent with the outage you experienced, though it wouldn't be surprising to see just from normal age related wear and tear for a 2007 model either, as this set is well past its service life at this point.
The one thing you may attempt yourself is to fully reset the system:
1) unplug both power and phone lines from the main base.
2) remove batteries from all handsets
3) wait at least 15 minutes, then restore all
4) place a handset on the main base for a minute, as if to charge
5) check for functionality.
If the problem persists after this, it tends to confirm a hardware failure which would require repairs to correct. Unfortunately once the 1 year warranty is up, repairs are not practical, and the base alone cannot be replaced. The most economical option in this case is to replace the entire system: http://amzn.to/1OVuHg5
Best regards, ***** ***** for the news,
I am an independent technician and I've spent my personal time, unpaid, in an effort to assist with the question for which you solicited my services. This site works on the honor system, and to that end, I have prioritized working with you ahead of other paying customers.
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