My Panasonic Plasma is also over 13 years old and still working great. It's survived the few power outages over the years but I always disconnect power to my AV devices during a black out and wait for stable power for turning things back on again. A battery backup supply or regulator as suggested is always a good idea for sensitive electronics if you don't have surge supression or have unreliable power, although NA grids are pretty stable.
As to the op's question, that depends on whether you have a reputable repair technician in your area. Some don't like to work on flat panel TVs due to the size, but a power supply repair should not be a huge expense with an experienced tech. You have to weigh the cost vs a new TV, depending on what you can afford. Plasma's have a wide viewing angle and relatively deep blacks, so would you be happy with an inexpensive LCD or would you need to step up to a QLED or OLED to get the same or better picture quality? That plasma will be 1080p so a new TV will be at least 4k and with modern upscaling the image will be better even with 1080 sources. This may be an opportunity to upgrade to a larger set as well.