The only way of really getting other harddrives to work on other machines is by having the same make, such as owning a dell laptop and another dell laptop and taking the HDD out and putting it into the dell it will work, but taking a harddrive out of a dell and putting it into a compaq will make a blue screen error which in your case will happen since it's from laptop to desktop..
So no.. not really, but yes you can give it a shot, nobody said it won't work it's just it shouldn't work...
Have you heard of a USB PEN drive.. it's a little device that can save info on and transfer to other computers:
4Gb USB Pen Drive Flash Memory Stick SANDISK CRUZER | eBay
Something like the above..
You can get windows 7 but it's against the law to use a cracked version, I would suggest this, your laptop harddrive is a small 3.5inch HDD, which hopefully is sata.. order a usb pendrive and save everything from the pen drive and store it on a friends computer or family members, just for your own confirmation that it's secure, and then use your old harddrive and use a windows disk in the new machine, it is all possible but only with the correct equipment.