Well… It turns out that my ISP provider did change some settings when the added the static IP address, that conflicted with my MX. The error was that the modem was replying to some requests, ICMP was one, so after some (many) hours of frustrations, I could count the MX out of the source of problem.
The bad thing is now the ISP are not sure why my modem in transparent mode isn’t transparent…
Thanks for your effort in helping, it gave me the fresh eyes I needed… Now I hope they can fix the modem…