Alright, correct me if I have misunderstood anything:
1.) Your Internet Service Provider (ISP) uses DSL - way faster than dial-up even though it is through your phone line.
2.) You have a wireless router and your laptop can wirelessly access the Internet through it.
3.) In a building separate from the house, you have a desktop PC, yet no direct line to connect to the Internet.
4.) You therefor want to connect your desktop PC to the Internet wirelessly.
To do so, you will need a
wireless network adapter installed in your desktop PC. Note how some adapters have clearly visible antennas while others look strikingly similar to
the typical flash drive. It is unlikely that your desktop PC already has a wireless adapter, but go ahead and look for antennas at the back of the computer and the USB ports as well.
Before buying a wireless networking adapter for your desktop PC, be sure that your router is broadcasting a strong enough signal to reach the building in which your desktop PC resides. Your laptop will not actually be involved in connecting your desktop PC to the Internet, but we can use your laptop to check the routers signal strength in remote building.
So go ahead and bring your laptop to the building in which your desktop PC currently is and see if your laptop can still access the Internet just fine. Try watching a few Youtube videos and see if it still loads at roughly the same speed it typically does when your laptop is in your house.
If everything works great, then
I recommend you purchase this particular wireless networking adapter for your desktop PC. It is incredibly easy to install since it is a USB adapter instead of a PCI one. You shouldn't have any issues with signal strength, assuming that even your laptop can browse the net just fine from that remote building. Finally, that particular wireless networking adapter has a 300 MB/s transfer rate, which is nice to have in case you ever go with cable Internet instead of DSL.
Best of luck and enjoy!