Internet drops a few minutes after each reset, what to do?

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Hello,
I am desperately trying to find a solution. I've chatted with many agents, already, and even a Videotron technician came today, but my problem still persists.
My internet has been working fine for months, then it suddenly dropped. My devices can still connect to the network just fine, but none of them can access any resource on the internet. That is until I reset the modem, but then, the internet drops again about 1 to 5 minutes after each reset.
What's weird is that I can still manage to ping domain names (e.g. ping google.com) and I get a response from the resolved IP address. But I am unable to browse anything on the internet. This applies to both wifi and ethernet connections.
All the lights on the modem are fine and normal. So to the support agents, everything seems fine...
These are the things I tried (many times):
- factory reset modem, via web interface and the reset button
- reboot the modem
- disabled band steering
- connect only one device via Ethernet
- tried 3 different coax outlets in my house
- disable wifi, only using ethernet
- changed the modem's default dns settings to use Google's (8.8.8.8 and 8.8.4.4)
- used different ethernet cables
- switched the ends of the coax cable
- tried different power outlets
- tried different ethernet ports
- tried a new modem
A technician even came this morning to check it out. With my luck, at the exact moment the technician arrived, the internet started to work again before he even did anything! The technician was still nice enough to do some tests, and even installed a new modem for me. I tested the connection, and it seemed fine. Of course, 5 minutes after the technician had left, the problem snowed up again.
I am really desperate for a solution, as I need internet to work...
Thanks

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