If I were you id just buy a wifi extender, that would be the cheapest option. Id assume you already have a wireless card in your pc? This is the range extender that I have and you just replace the antenna on your wireless card with it
Alright. This is the exact one I'm using:
http://www.osxwifi.com/apple-broadcom-bcm94360cd-802-11-a-b-g-n-ac-bluetooth-4-0-with-adapter-for-pc-hackintosh
Bought on Amazon though.
And this is the extender; if you live in the first world, then you can give it a shot to the card and see if you need the extender or not, otherwise it may be wise to order it altogether at once:
https://www.amazon.com/gp/product/B0034CQSKW
Ignore what they say about crossover cables -- modern NIC's don't need that.
I'm also assuming you're using Windows.
I misread your post, you will need an Ethernet cable to connect your desktop to the laptop, otherwise this won't work the way I'm describing it. You could set up your laptop as a repeater or some other setup, but I'm not familiar with that.
Maybe look into an external antenna
Three of these. Actually 8dBi but were labeled as 9 when I got them.
These are true 9dBi gain and are cheaper but have no extension cable and magnetic wall stand.
Vertical range will decrease, your connection will be more susceptible to wireless background noise, and your devices need the transmit range to send data, so larger antenna doesn't help past a certain point unless both ends have them. They will help in any scenario but a good wireless access point will be the better investment if you have a 3 story house or live in a dense urban area.
The best way to improve range for free is to put your wireless access point in the most central location possible.