To be honest, I do not know about items of different frequencies interfering wirh each other but:

Does the cable have a ferrite filter?

For other people who fear interference from PCs:
The case being painted makes little difference to EMI and they are normally grounded with the screws, especially when 'starlock washers' are used to bite through paint and into the metal.
However a case painted inside could not be making contact along its edges with other parts of the case (like the base) and the Faradat cage can have 'big holes'. In the form of slits, these holes are worse at emitting (and receiving) amplified interfence.

I design enclosures for IT equipment, that is how I know.

A while back I ran into a weird EMI interference issue between my cell phone and a new custom built PC inside of a Cooler Master CM690 KKN2 case. When the PC booted to Windows calls would drop on all cell phones nearby, whether 3G, LTE, on Verizon or AT&T and they could not connect to any mobile networks. (Nobody in my office has T-Mobile, so we don’t know if they would have been affected too)

I spent a lot of time googling and couldn’t find any solutions. I eventually figured out what was causing it and wanted to post something here in case others are having the same issue. I assumed the high airflow case meant it was poorly shielding EMI from inside the case. It also has a painted interior and I don’t think the shell was grounded. I tried swapping out every single component and cable inside and even swapped out the case, but It turns out all that was completely unrelated.

There was some kind of interaction between my PC’s DVI cable and the NEC monitor it was connected to, and only at a refresh rate of 59 Hz. When I switched to 60 Hz or if I plugged into a different monitor the problem went away completely.

What I still don’t understand is how can a low frequency DVI signal (max clock rate at 165 Mhz) interfere with multiple high frequency cell phone bands (800Mhz to 1700Mhz). I’d love to hear from someone with hardware knowledge of the DVI spec if they have any theories on why this was happening.