Low Pass Filters...anyone has it on your station?

Doubt the LPF would help. Try repositioning the internet connection and router, add ferrites to those connections. Are you using DSL, cable, or fiber for the service? Ferrites on power supplies, too. Ensure you have a good RF ground on the rig.

If you were running 'big power' (not 30-40 watts) and you had horrible SWR with a lot of RF coming back into the shack, there might be some benefit to a low pass filter, but it's doubtful. Ferrites on power cord for router should help.

Now that I am at a keyboard.  An HF LPF filter limits or reduces the RF emanating from your HF rig above 30Mhz.  Back in the days about 50 years ago, it was a must have as HF rigs (kits) did not have the same harmonic reduction they have today or since about 1990.  

With your problem, it is an RF overload issue and that RF getting into your router, likely through the DC power cord.  From there it is getting rectified and then that is affecting the CPU on the router.  The RF energy is coming from your HF antenna, and that is doing exactly what you want it to do.  Let out all the RF energy so you can go play.

In your shack, you have all these other receiving antennas, called DC power cords and LAN cables.  Your HF RF energy hits these and are ultimately affecting your router.

You'll need to make sure you Ferrite Beads are the right type to block HF currents.  Those may or may not be the ones you have handy.  Give them a try and if they work, that is awesome.  If not, they may be the wrong 'mix'.  

I bet your easy fix is to just replace the router as it has bad ground bonding.  

BTW, I bet it is also RF noisy making it harder for you to hear HF stations.  The same chokes will help with that.

This document is worth the read for anyone who does HF operating:

 http://www.yccc.org/Articles/W1HIS/CommonModeChokesW1HIS2006Apr06.pdf

Mike va3mw