Wrap it in t-shirts

Remove HDDs just leave the SSD in. Remove the cooler if you are using a large air cooler. Bring a little thermal paste and a screwdriver to reattach it when you get to LAN. Wrap your monitor in a comforter. Remove the stand if easily possible. Lay the tower flat on its side mobo side down for the trip. If this is not possible remove the GPU as well if you have a large high end card and carry it in your bag with the CPU cooler. Wrap the CPU cooler and GPU in newspaper to prevent damage in your bag. Use the anti static bag that came with your GPU if you still have it but it should still be fine regardless.

Just put the case down on your backseat in such a way that the videocard and CPU cooler are facing up, maybe wrapped in a blanket, surrounded by other crap so it can't move around too much. That's all.

Never had any issues in over 20 years of travelling to LAN parties, including 8 hour trips to England.

i drove my computer 3000 miles by putting a seatbelt on it and setting it on top of a pillow, and putting my monitor and keyboard etc in a bag

Be extra careful with the monitor, you dont want some crystals to break in the middle. A blanket/thick bubble wrap is a good option

i drove my monitor and pc cross-state and put a seat belt across it. it made it and i didn't remove anything
not saying you should do this.
if you have your case box / monitor box, use those and hope for the best

HDDs REALLY do not like being bounced around and large air coolers can cause microfractures in the mobo if bounced in shipping (i have personally had a mobo die this way). There is a reason OEMs use AIOs in high end systems despite there worse long term failure rates and when they ship them the case is filled with foam.

Had a friend last year whos gfx card broke just by transport his pc on a trolley, take that shit out.

wrap each component individually w/ bubble wrap, leave mobo inside case. wrap monitor in a bunch of towels