Seems I lucked out there as the A31p's P4-M has SSE2, for what good it can do. Your 7500 driver works like a charm (FireGL 7800 is a 7500), although there is a warning triangle for the Philips WDM Video Decoder which I believe is a feature of the FireGL, not sure for what precisely. I have favor for the XP theme but don't particularly want XP, so I have a theme patcher applied and a custom Luna theme I got on deviantart years ago, along with old classic shell 4.2.5's two column Luna skin (latest version of open shell doesn't play well with my theme patcher). A31p doesn't have a TPM but Bitlocker has an alternate non-TPM mode where a USB startup key must be present at bootup instead. So some passive "security" is possible on this nearly 21 year old computer after all (build date reads 03/06, shortly after the introduction of the T40).
To get audio to work I needed to use the Windows XP "Audio driver for Windows XP, 2000, 98SE - ThinkPad R40, R50, R50e, R50p, R51, T40, T40p, T41, T41p, T42, T42p, X31, X32, X40" from
https://support.lenovo.com/us/en/downloads/ds013790 or found in the drives page above. Even though A31p is not listed, it works and is the only one that will work for 7. The official A31p drivers seem to only go up to NT 4.0 and while they work on XP are incompatible with Vista/7.
Now I just need a working WLAN card, or I can hookup via 100mb/s Fast Ethernet, and this A31p can browse the internet again.

I am unfortunately encountering immobilizing system freezes. I'm hoping it's just an OS setup issue rather than a latent hardware failure considering I never encountered this with my XP environment, which is in another partition on the SSD and could be dualbooted for further testing.
The other impressive thing is the Sanyo battery manufactured in 2001, first used in 2005, is only down to 22wh from 43, so close to a T470's internal battery. Speedstep coming in clutch here.
Well enough about A31p and back to R40.