Mission Impossible?

[Gorman]

I just purchased a refurbished desktop computer and would like to transfer gigabytes of files to it from my old laptop.

I am thinking about networking the two together which is something I know nothing about.

Added to my total ignorance in this matter are two more hurdles.

The laptop's network card was ruined by lightning and can only connect wirelessly or I would buy or make a cable for this.
The laptop os is Windows Vista Home Premium/

The desktop has no wireless adapter at all that I can find in the device manager.
The desktop Os is Windows 7 Home Premium


The laptop connects to the internet just fine wirlessly.

The desktop is plugged into the wireless router and connects to the internet as well.

Is what I am trying to do possible under these conditions?