Another option is if the machine has a serial port that might be dumping useful info as it boots. A serial to USB cable is really cheap and you can read it with PuTTY.
If you don’t want to deal with the used market (which might be necessary to get super cheap) the Intel Arc a310 cards have HDMI/Display Port and are slot powered so no PCIe power needed. They’re also sought after for their quite good video transcoding performance so reselling it after you’re done would be pretty easy.
Nice, another good option. Hope you have luck debugging your machine!