Mac mini wifi REALLY slow???

I'm at my wits end here and praying someone has an answer.

I bought a Mac Mini last month (with maximum possible RAM, processor, hard drive, etc.) to replace my old iMac and the internet connection is abysmal. Sometimes it just completely drops out and cannot load a webpage at all, and when it does manage to stay connected it is horrendously slow. Speedtest says my download speed is less than 5mbps. Other devices in the house are all 40+mbps! Some even over 100!

We have just changed to Virgin Media today, and the problem has continued as it was on my previous BT Broadband. As I said, all other devices are working perfectly, including the Windows laptop I'm using to submit this which is sat right next to the Mini. It is definitely not a problem with the network, as the problem is only on the one device and has happened on two different networks.

I have tried every **** suggestion I could find on the internet. I've reset again and again, cleared the cache, adjusted the DNS settings, set up the network manually, deleted the old preference files under SystemConfiguration, adjusted the Bluetooth settings, and nothing has helped.

Whenever I try and load a webpage, it says "resolving hosts" in the bottom corner. Another notable thing is that airport always seems to be "looking for networks" though it is already connected to the network I want.

Is there some way I can possibly fix this? Would purchasing an Airport Extreme help? I'm nowhere near my router so can't use ethernet, but I'm willing to use a cable to any kind of extender/other router that could get this **** thing to work. Or is my Mini really just faulty and should I just go book an appointment at the Genius bar???