It's surprising how many power strips and battery backup systems go bad. Sometimes, the symptoms you're reporting occur when they start to fail.. They're not expensive and easy to replace.
Hope this helps.
Grif
My modem and router don't always turn on when I turn on the power strip. Loose wire somewhere? When I asked a question years ago, I received many answers, but no one mentioned to tighten the power cord so I learned that sometimes the answer is something so simple that it is overlooked! I always shut the power strip off when I am done using my desktop, but now I am afraid to shut it off thinking I may not get it to work again. Thank you for your advice!

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic