I have an amiga 500, and was transferring some files to it when I started hearing a strange noise. It was like a pulsating alarm clock. This noise happens whenever I do any sort of serial communication. Even when I just hit refresh on Amiga Explorer. It lasts the duration of the serial communication. It is output from the amiga via the rca jacks I am fairly certain as it comes into my computer via my line in. I have attached a sound recording. This is the amiga when I am transferring an adf to floppy over the serial port. The serial port seems to function normally.
Note that the static/noise is not from the Amiga but from my dirt-cheap Sabrent capture card:)
There's all sorts of crosstalk noise you get from the old hardware. I once started work on a joke glitch track in OctaMED called "Songs of the blitter" using samples of the strange audio background I got from just moving windows around and scrolling

I think the problem was always there but far less noticeable when the kit was new. More than likely various decoupling capacitors have dried out, allowing more interference through. Also, I guess that in my case, not having any RF shielding over the motherboard contributes to induced noise from other hardware too.