TLDR: Its a Its probably ONT or ONR, essentially a modem (ONT) or modem router (ONR) for fibre based internet. Its what I think you are or were getting internet off of.
It shouldn't be connected to your modem. It should be connected to a router. If you have two modems, both connected to your internet, there's going to to be issues if they're plugged into each other.
Thanks to the excellent sluthing by Giacomo1968 and LawrenceC - its apparently a NOKIA 7368.
The connection to the left of your photo, with the thin yellow cable is a fibre optic connection, typically a GPON interface using a APC/SPC connector. (and I see a laser/do not look at light with remaining eye warning - which confirms this). These things are fairly typical for gigabit/fibre internet connections.
Fundamentally - if you don't know what this is leave it alone. You're probably better off tracing and labelling the cables you have and understanding your network rather than disconnecting random things and scream testing
I found the manual for this online after someone found the model
The little covered bit with the laser logo is a fibre optic connection with a similar laser warning - . The ntwrk light should be on solidly and the optical cable is a bit fragile. If its not lit - well firstly make sure you have fibre optic network. IIRC the ISP tends to 'activate' a port on the wall end, so you can't swap that, and the only potential issue is a broken fibre optic cable.
You can probably check the LEDs to troubleshoot as per this table. The NTWK light SHOULD be solid (more typically its called PON) and the fail light shouldn't be red. It does look that everything is ok and its connected to the internet.