Advice on upgrading T5610 GPU

Don't worry too much about listing of compatibility.  Just pay attention at the fitment, power requirements, power connector availability, and your usage needs.

This is the spec-sheet for your system if you don't have it already.  Use the Quadro K5000 as a guide for the fitments if you are looking at a full height, full length card.  If you plan to use a card that require external power connector(s), check your power supply to see if you have x2 of 6-pin connectors or x2 of 8-pin connectors.

Although newer cards will be backward compatible, you can't take full advantage of PCIe gen4 as your system has PCIe gen 3 slots.

With all that said, I hope you can make a better choice for your upgrade.

Intruding. You could find a RTX A2000 for less than 400usd, and that one is more recent and powerful than a T1000 ( obviously if having 2 slots used isn't an issue )

After looking at prices, I decided to go with the T1000. After I installed it, the machine would not boot. It came up with the normal POST splash screen (using the T1000) and the RAID splash screen, and then just hung.

So I reinstalled the original K2200. Same problem.

After scratching my head a bit, I have tentatively concluded that there was something else wrong that was about to fail anyway. The reason I say that is that for the past couple of weeks, the machine would not always boot reliably. Typically it would go through the splash screens as described above, then hang. Pressing CTRL-ALT-DEL would cause a brief horizontal line to flicker on the screen, and then the hard drives would spool down, the machine would reboot, and everything would continue normally.

After I swapped in the T1000, pressing CTRL-ALT-DEL would cause the machine to reboot and the hard drives to spool down again, but it would never get any further. And similarly after putting the K2200 back.

So at this point, I concluded that there was a separate problem. It's not with any of the drives or their controllers, because the RST controller was seeing them all. Moreover, I could bring up the BIOS configuration screens. However, when I tried to run the BIOS diagnostics, it just hung.

This machine is about eight years old, and the reason I was going to install the T1000 was that its GPU capacity was inadequate for the new Adobe Lightroom Classic denoise function. Moreover, it is not capable of supporting Windows 11, which means from a pragmatic viewpoint that I will have to replace it in the next coupld of years no matter what.

So I returned the T1000 for a refund and am now in the process of putting together an order for a Precision 3660, which I hope will get me through the next 6-8 years. Those who are interested in following my saga will find that I've asked a few other questions in this forum already.

Sorry to hear the repurpose plan does not work out.  A cheap test can be perform, replace the coin cell battery with a new CR 2032 and reset CMOS with jumper.  Then run a diagnostics scan again.

@Chino de Oro​ What does resetting the CMOS do? I would think that if the battery has run out, it would reset itself.

@Chino de Oro​ I replaced the battery. The manual says nothing about a jumper to reset the CMOS, but does say that the NVRAM (which I am assuming is the same thing) will be reset by replacing the battery.

When I tried booting the machine after the battery replacement, it complained about an invalid configuration and said to hit F5 to reset, which I did. That took me to the BIOS, which asked me to enter the date and time. I went through the rest of the BIOS configuration and all looked reasonable.

When I tried booting again, the same thing happened as before: Dell splash screen, RAID splash screen, then nothing. I tried again, this time hitting F2 before the Dell splash screen, and successfully entered BIOS. Selected "reset all to defaults," which it did. I verified that things like the RAID configuration and Windows Boot Manager were set appropriately and tried again.

Still no joy. Any more ideas, or do I go ahead with my plans to replace the machine?

NVRAM or CMOS, it just refers to the memory section that store value of BIOS settings.  By removing battery, that will clear NVRAM back to default settings.  Using the jumper will remove, reset additional cells which stored password and remaining options in advanced settings.  Seeing the convenient of some extra seconds moving the jumper during the battery replacement, it does not hurt to do both.

Temporarily removing (unplugged) all storage drives and RAID controller.  Run a diagnostics scan as mentioned earlier.  If no error, using a spare drive and testing with a Windows installation to see how your machine hardware can be functioning.  Use Windows Creation Tool to make installation USB.

With the machine is still functioning, having power, gaining access to BIOS, you have to evaluate your needs and decide if you want to fix the current one or getting a new machine.

Shared a few tips on other thread in helping with options selection during purchase.   

I tried clearing the NVRAM with the jumpers (which turned out to be in a completely different place than described in the generic document you posted--fortunately there was a placard inside the lid that told me where to look). No change in behavior.

So I am continuing with my plan to replace the machine outright--though I must say that the level of sales support I'm getting from Dell right now is low enough that I am seriously considering a different manufacturer.