I've got a TI 486SXL-40 that was purchased as-is several months ago and so far haven't gotten to POST. It's in good cosmetic condition and I assumed it wasn't dead, but it's failed to POST in the several boards I've tried it in. (starting with my OPTi 495SX based 3486 board then a Soyo SiS 471 and possibly an SiS 496 based board)
All attempted at 5V (except the 496 board which would have been at 3.46V at the time) and tried at lower speeds with no POST, so I assumed it was either dead or very picky about what board to use.
Much more recently I picked up a Ti SXL2-66 which so far has also failed to POST in 3 SiS based Socket 3 boards and a Symphony chipset 3486 board set to 486SX and then DX mode. (and I've stopped swapping CPUs into the OPTi board for now as it's in a fairly cramed AT case and I've ended up bending pins while extracting CPUs: I'll use it for testing again when I swap another board into there)
The SXL2-66 was also purchased as-is, but supposedly was pulled from a board in working condition many years ago and left in storage, so seemed likely to be fine. (print and heatsink were in good shape, though pins needed a little adjusting, I think some happened in transit due to lots of padding, but not much rigidity)
However, I don't believe I attempted to run either of these CPUs with a 3486 board set to 386 (or 486DLC) mode, and I've also found that many of the CPU-model/version specific jumpers don't impact things much while others are required so long as all those are the same socket type, while the socket-select ones are much more important. (386 settings work for DLC CPUs, 486SX and DX settings often work for SX or DX CPUs, though DX CPUs seem to be the least picky)
In any case, I don't think I ever tried using 386 (or 486DLC) jumper select settings for one of these Ti PGA-168 socket CPUs, but maybe that could impact things. (I suppose if it's an issue with differences in bus protocol, that could make the difference)
The boards I have might be too old and too new to explicitly list the PGA-168 SLX or Cyrix 486S CPUs. I have 3 386/486 boards now and manuals with 2 of them (the OPTi 495SX and UMC based US 3486), and no mention of these models. I think only the OPTi 3486 manual explicitly mentions the Cyrix or TI 486DLC, though with that board I haven't found any functional or benchmark performance difference between the 386 and 486DLC settings when a DLC is installed. (OTOH, Cyrix 486DX2, IBM DX2 BLs, and ST's DX4 CPUs seem to have no problems running at 5V as 486DX CPUs in these 1991 or 1992 boards)
I'll have to try again with the TI PGA168 CPUs with 386 or 486DLC mode set and see if that does anything. I'd made the assumption those jumpers were socket-specific selections, but given the boards tend to not work at all when both CPU sockets are populated, it makes some sense that both sockets are still active on the I/O side of things. (I remember getting the OPTI board to post in 486DX mode with both sockets populated at one point, but may be wrong and did not attempt to boot an OS at the time: it was also quite clear that both sockets remained powered and should be cooled accordingly: aside maybe from a 386DX and some low-clocked 486s ... I'm certainly not keen on using a DLC at 33 or 40 MHz without heatsink on it)
I considered getting a known-good SXL PGA168 CPU for testing purposes, but it seemed like a not-great investment at around $30 shipped on the low end there. (a few as-is auctions have gone for less, but that wouldn't solve my problem)
I was actually hoping the SXL2-66 would behave more like a Cyrix DX2-66 and be pretty hassle free, compatible with early (or at least Early non-Intel 486) and late gen 486 boards and apparently tolerant of a wide range of voltages while also being pretty overclockable. (the Cyrix/IBM/ST DX2 and Intel DX seem to be the most flexible models I've tried there: that goes for Intel DX-33 and DX-50 CPUs working at 3.3 or 3.45V without issues)
Instead, it seems like they may behave more like DLC/DRX type CPUs just in the PGA-168 socket, and rather being plug-in compatible with typical Intel and AMD 486 compatible boards, might just be for 386/486 chipsets/boards that omit the 386DX and 387DX sockets for a cheaper, simpler layout but the same 386-bus mode compatibility requirements. IBM's SLC/DLC and BL 386-derived CPUs probably relied on chipset and board layouts like those too, but they were all mated pairs, so matching CPU to board isn't the same sort of variable.
And I don't have a bunch of working 386 socket boards to try the 486DLCs in, but so far they've been pretty hassle free too, albeit given the lack of 'Heatsink and Fan Required' on the package label, I wonder if these were typically used without a heatsink or fan (beyond case mounted fan) as they get extremely hot when left bare and without excessive airflow. (they do seem to work when burning hot, but it can't be good for them, or especially some other components in the case ... especially electrolytic capacitors or even the plastic of the socket itself)
I'm going to assume the (much less common) TI 486SXL CPUs in PGA-132 form factor are mostly plug-in compatible in 386 or 486/486 boards without some of the quirks of these PGA-168 CPUs.
Hmm, but come to think of it, if these SXL CPUs are fully electrically compatible with the 386 bus, they could potentially be adapted back to the PGA-132 socket via an interposer/adapder board.
Maybe Socket-2 boards would be in the right age range for supporting these sorts of CPUs as well. I do have a Biostar Bioteq board that looks like Socket 2, though it still needs a BIOS replacement. (got it to post with a mis-matched BIOS and is in good cosmetic condition, but currently not useable otherwise)