Hi. My desktop is seven years old but has worked well (despite the growing niggles on some sites caused by the combination of XP/IE8).
Down speed (delivered via fibre optic to the nearby neighbourhood control box of ISP provider - British Telecomm - fell to 4.95 mb just now.
One phone line cable from the wall goes to the telephones, the other to the DSL port of my router. A red cable from LAN1 port of the router goes to my modem.
If I disconnect that red cable from my modem and plug it in my laptop, the downspeed is 32 mb.
I also have a wireless dongle in my desktop for my printer. I took that out and lost broadband - I put it back in and got broadband.
By the way, I didn't get any 'cable unplugged' messages.
So it seems to me that the problem is not the modem nor the router but my desktop.
If it is my desktop, is there anything in my desktop's software/hardware that I can check, please?