Unplug the hard drive from the new desktop and plug it to the laptop using something like:
Then, download this tool:
(there's plenty tools there, this is just an example)
Once the tool is installed, you can clone the laptop disk to desktop new disk. Might take sometimes to close. Also, if the laptop disk is bigger than the new drive this won't work. Make sure you have enough space on the desktop disk. If the target disk will have the same configuration of the laptop disk so if you get a 1TB as the desktop disk and the laptop disk is 120GB then you will end-up with 120GB on the desktop disk, you can use some tools to create another partition or resize the disk once its back to the new desktop.
Now, once the disk is cloned, plug it back to the desktop and boot. You will get some errors on the start-up because windows does not recognise any drivers. You will have to re-install all drivers for the new desktop. After few reboots and all driver installed, everything should boot up nicely.
NOTE: this solution is not 100% guarantee, make some backup just in case you have to fresh install windows on the desktop.