|Your modem is borked!|
That was my broad hint.
You said, "All routers work on LAN side, just will not connect to cable modem"
Since all routers you tried worked on the LAN side, then that leaves the WAN side as being the issue.
Since you tried multiple routers with the exact same results, that rules out the routers themselves and leaves you with whatever us upstream of the router.
The next thing to check is the network cable between modem and router. If it's good, the very next thing that is likely to be bad is the modem.
I suspect the issue is the modem. If it's provided by your ISP then call them and get another to test. If it turns out to be not the modem, then that leaves your provider as being the issue.
If you have to purchase your own modem's like some ISP's make clients do, first make sure you can return it if it turns out to not be a problem with the modem. If you can return it, get a new one and test. If your internet starts working, you resolved the issue. If it doesn't, then as I said in the paragraph above this one, the issue is your provider's and you need to contact them.