|Call your ISP back, explain that you have tried another router and it didn't work. Then, ask them to please replace the modem as it seems that must have failed.|
Do yourself a favor, buy a small UPS and plug your router into it. If you can afford it, get them for your computer(s) and home theatre system too. Not only will a good one provide some run-time on battery so you can gracefully shut stuff down, it will also provide power conditioning and protection against surges, spikes, and brown outs.
Here's an example of what I'm talking about:
Alternatively, a real surge suppressor, as compared to the 'power bars' sold most places which don't do squat.
Read APC's warranty and you'll see why I not only recommend them, but use their equipment extensively both at home and at work.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.