my answer does not have steps to 100% solve your issue. but it should help you to narrow it down or find a guilty one.
The 1st thing is to find out if this is a hardware problem or software.
To ensure this is not a hardware problem, you (ideally) need to put MSWin (either live or fully installed) on your new PC. And then do your test.
- test does not pass - means a high probability of buggy hardware. There is also some (small) chance that failed test does not mean bad hardware. Bugs in firmware might be the case
- test passes - means hardware is ok. You need to move to software tests.
I tend to believe its a software thing
The 2nd thing is to find out which software piece does not do its job.
I see two pieces that might be involved here: the Linux kernel itself and the driver for integrated video card. You need to check both of them to see if they support your hardware (CPU generation, chipset, GPU, etc). There are 3 possible cases here
- super luck -- support of it is in already released versions. You need to find and install those versions.
- tiny luck -- support of it has been committed but not released. You need to find and install those snapshots.
- no support has been added yet. You need to wait and follow their mailing list, GitHub, or whatever they use.
Off-top: did you check if that PC has the official support of any Linux distro before buying it?