My Pentium P5-60 had gotten some circuitry fried in when I connected a printer to a power source without a surge supressor and the connection got a spark at the wall, the PC rebooted luckily, though, the floppy disk connected to the motherboard stopped working, the printer stopped printing, and later the ISA IDE part of the Intel Batman motherboard stopped working, though the rest of the computer continued working.
I am the original owner of the computer and so when the Dallas RTC battery went dead, I pushed a key for resume, had a heart attack as time went by and it screen had nothing on it, and then, it started going through the boot process.
Not sure if this can work for you, but I later wanted to put the original Windows 3.11 WFW workgroup edition back on a 540 MB HDD so i could install a version of Matlab only compatible with windows 3.11. I used another PC to install MS-DOS 6.22 onto the 540 MB IDE HDD. I put the HD back in the P5-60, put an old CD-rom card and cd-rom drive in the PC, and was able to install the windows on it using the cd-rom.
Until you get your Dallas RTC battery problem corrected, you may can get it to boot with booting a boot image such as MS-DOS on your HD using another PC, and with patience and time, it may possibly boot then.
I am uncertain as to the logical explanation why it still works despite not having the BIOS batter working other than the settings in the BIOS may still allow it to boot if it has a MS-DOS boot sector on a HD Size compatible with the PC.
Have you gave a go yet at replacing or doing the chuck-mod on the RTC correcting the battery problem?
I bet a if you have a PC hobby friend that solders or anyone that does soldering work can help you with the chuck-mod, i think is what the procedure was called.
have fun@!