try reinstalling your ethernet / wireless drivers.
When someone downloads something small, there is next to no packet loss what so ever. When someone is downloading something large (like those 10+mb files you were talking about) there are bound to be a few corrupt / missing packets in the bunch. Its your ethernet drivers (wired or wireless) that are suppost to request a packet resend so you are not missing any part of said download or have any part of it being corrupt.
Since you said you had just built a new system, you might have used a modified version of windows (i know people who use them) or linux. Sometimes these modded operating systems might have corrupt TCP/IP drivers (which come pre installed with the OS) and you might have to re-install those as well.
okay, well maybe try mapping out one of your drives on your desktop, and just use your laptop to transfer everything. Its not hard, once you map out the drive in your network its as simple as saving the file to that drive, so the download will simply pass through your laptop and onto your desktop.
As for your downloading problems, i would check your router. Log into it and see if there are any settings that may have been accidentally be enabled or something. Try and using someone elses router and see if there is a difference or not. I dont know what else to tell you, you've really stumped me