1. If you have a home that was built within the last 15 years or so, check behind a wallplate that has an existing cable or phone connection on it. Look for additional cable and ethernet cabling behind the wallplate. That would indicate that you have structured wiring built into the home but not completed. That Structured wiring bundle is comprised of two RG-6 cables for satellite, Cat-5e or Cat-6 for ethernet and one Cat-3 (possibly Cat-5) for telephones. If that is present, it could make this much simpler.
2. If you only have a cable connection near the desk, you could consider MoCA adapters such as this to run ethernet to the desk:
The latest trial firmware for the CODA-4582 contains MoCA 2.0 capability, so, you could conceivably only need to buy one adapter. There are a couple of items to keep in mind that I can lay out later.
3. If the room that the Modem was located in, and the room that the desk was sitting in were run off of the same side of the electrical power panel, you could consider powerline adapters as well. The latest version of these is the Homeplug AV2 adapters, which use all three of the electrical lines, line, ground and neutral to run data:
4. Fwiw, the CODA-4582 does not have transmit beamforming enabled. You could consider going the route of adding a router which runs 802.11ac, giving you the capability to run transmit beamforming for 5 Ghz 802.11ac. That might help connecting directly to the desktop wifi nic card. Out of curiosity, what card did you buy? Are the antenna located off of the card at the back of the pc, or are they on top of the desk, connected via antenna cable to the nic card? I only ever recommend routers with external antenna in order to get the antenna away from any shielding or interference from the router itself. My personal preference for an all in one router is an Asus router, fwif.
5. Depending on the performance of the nic card and its antenna, you could also consider adding a router at the desk location and run that router in Bridge mode. That not the same as the modem's Bridge mode. A router in Bridge mode acts as the second half of a wifi Bridge back to the modem, similar to what your extender is doing now, but, its has the benefit of external antenna and much faster processing.
So, there are some options, its a matter of how important reliable internet access is at your desk, and how much you want to spend to achieve that. First thing I would do is sort out the wifi environment that your in. Maybe switching channels might help. If you can run the wifi network in the channel 149 to 161 range that would probably help. Running 802.11ac would also help. After that I would look at the issue of any additional cabling which might be hidden behind the wallplates and at the structured wiring cabinet, and then consider MoCA adapters which can run over the cable system in your home.