When i click on detect, this is what i get.
You then click on that display-not-detected rectangle to work with it, then scroll down to find the "No display detected" box which you change to "Try to connect anyway on: VGA"
If you aren't even seeing that display-not-detected come up, i would point to a driver issue. That 9250 is twenty years old now and the latest drivers for it work with XP, according to AMD's website. To use a newer OS, you might need to grab an updated card like a Radeon 7450 or low end R5 card. I prefer AMD for these builds as you can use crt_emudriver as a fallback, just in case. Just make sure it has either VGA or a DVI-
I port, not DVI-D (which last is digital only). Or plan to buy a HDMI-to-VGA converter or similar, which are pretty cheap, but also a mixed bag in terms of quality.
Or you could go back to XP, if your new machine will let you install it. But this probably means hunting down older MAME versions and roms as well. And any other emulators, frontends, drivers, etc.
EDIT: Hmmm, you might be able to use safe-mode to get in as well. Most PC's would default to outputting video through the VGA port if no display was detected. But it might not be at 480p or 600p - hence, safe mode. You'd probably need to tell the PC to reboot in safe mode from the working monitor. TBH i'm not sure exactly how this would work.