''the Core i9-10850K uses the integrated Intel UHD Graphics 630 chipset''

Usually CPU's with designations like ''F'' or ''KF'' don't have integrated graphics. It could be possible that the iGPU was disabled in the BIOS so it might be worth checking that if whoever built it decided to turn that option off but if you're not getting a splash screen/video output to begin with and ya don't feel comfortable using ya graphics card then ya might also want to try ressetting the BIOS either by removing the CMOS battery for a couple of hours and/or by looking up ya motherboards instructions on how to reset ya BIOS manually (usually by touching/bridging certain pins on the motherboard with a screwdriver; while the system is off and disconnected from the power supply of course.)

It could also be possible that the HDMI port is being temperamental/not being detected by the monitor upon start up and is outputting through the other ports (VGA/DVI) on the motherboard instead. Don't ask me why but sometimes it's the monitor failing to detect a signal from the board or vice versa or dodgy cables/outdated drivers etc. I had similar issues with HDMI not always being detected and the board outputting through the VGA/DVI ports by default instead or it sometimes taking several reboots for the monitor to pick it up through the HDMI cos I'd hear it boot up correctly but still no video on screen.

Often times things are just a matter of trial and error. I once had a PC that refused to boot up for 2yrs after a random power cut. I took the thing apart multiple times and put it back together again and it seemed like the PSU was dead or faulty. Then one day I tested it wth another PSU which was too underpowered for my GPU but was enough to power my board so I thought I'll try my old PSU one last time just to confirm it's dead before I buy a new one and suddenly it was working again. I still have no idea why it was acting so crazy (possibly something to do with the motherboards dual BIOS or something else I'd missed) but the PSU didn't have the best reputation and sometimes both sticks of RAM didn't show up so it could've been one thing or another or a combination of things. Sometimes it's worth testing with one stick of RAM in slot 2 before adding a second to slot 4. The important thing is just to get in there and don't be afraid to get hands on as the only way to learn is through trial and error. Just take ya tme and be thorough until it becomes second nature.

As others have said make sure ya RAM is plugged in correctly to the correct slots 2/4, replace that PSU ASAP!!! (do not reuse old cables with the new PSU and throw out old ones to avoid mixing them up) and try to clean that pin on ya card without damaging or loosening it especially if it's melted plastic on the pin.

Also make sure you get a good quality A Tier PSU from a reputable brand if ya can since that's often one of the most important parts especially when working with high end expensive graphics cards and will serve you into the future providing you get a good one which meets all of ya needs. An 850W PSU should be fine for the 3090 but ya may want to consider stepping it up to a 1000W+ PSU especially if ya plan on overclocking or upgrading to a 5090 at any point. Last but not least either google ''Cultists PSU Tier List'' or check out the most recent updated google doc below so you can cross reference any PSU's you might find before you buy if ya options are limited as even the most reputable brands i.e Gigabyte/Corsair have had issues in the past so it's always worth double checking.

https://docs.google.com/spreadsheets/d/1akCHL7Vhzk_EhrpIGkz8zTEvYfLDcaSpZRB6Xt6JWkc/edit?gid=1973454078#gid=1973454078