the rominator ii by @bigmessowires is also 32-bit clean, as it was designed originally with the iici and iisi in mind, but will fit and work in a iix, iicx, and SE/30
that sounds like something is broken with the system. Try booting from a System Tools disk and see if the behavior persists in the System Tools disk. If it doesn't persist, try running Disk First Aid on the volume you normally use to boot
and one more tip, frequent your local thrift stores, there are bound to be tons of displays capable of VGA that people are donating there, that's how I got the LCD monitor for mine
there are VGA to HDMI adapters on Amazon, and recapping the power supply is doable, make sure to discharge all the capacitors before attempting to recap the power supply, you don't want to get zapped by charged AC capacitors while you're soldering (which can be between 170V and 340V depending on...
I suspect a head crash. Since the drive isn't showing up on anything, open it up and see if you can see any obvious circular scratches as that would indicate a head crash, as that's the only failure mode I can think of that can make a drive delete itself from existence