And Welcome to Ubuntu Forums.Org!
I had the same problem when I purchased my Desktop.
If that continues you may want to give your Internet Service Provider a call and question the Representative as to what exactly is going on and why.
However the speed I have been getting is really really slow.
Ask for a Manager or a Supervisor if the Rep gives you some ridiculous answer.
You mentioned that you had to get a USB Adapter for your Desktop and your wireless to work. (I don't get why some manufacturer's don't include a NIC)
That's good but you may need a driver for it.
Go to the website of the manufacturer that made your adapter and look for a driver. Download the driver and install it on your system.
To install the driver you would use:
apt-get install <nameofdriver>
Hope this helps