Dell Precision T5600 with Dell X540-T2 10GB - Not Booting, Flashing Cursor

I have an ageing Dell Precison T5600 workstation I want to add to my 10GB fiber/copper network. I purchased a Dell-branded 10GB X540-T2 from Newegg (Dell P/N: K7H46) assuming it would have the highest chance of working with this system.

The T5600 in question is setup as follows:

Dual Xeon E5-2687W 8 Core CPUs
128GB RDIMM ECC 1333MHz DDR3 (8x16GB)
Quadro K4000
Dell (Intel) X540-T2 (Dell P/N: K7H46)
Dual Intel DC S3700 800GB SSD

The problem I am seeing is pretty simple. With the X540-T2 installed in any PCI-e slot, the system will pass the BIOS splash-screen (post) and just sit there forever with a flashing cursor in the upper left. You cannot enter the BIOS in this state, nor can you choose a boot option. The system WILL initialize itself upon first power just fine though, cycling back off. There are, however no lights on the X540-T2's ports, nor beeps or diagnostic codes from the system.

With the X540-T2 not installed, the system boots and works fine. I have, however, found that this exact Dell-branded X540-T2 works well in these systems and motherboards:

Dell Optiplex 5040
Dell Optiplex 3020
Dell Precision T1700
ASUS X99-E WS
ASUS P9X79-E WS

I have also tried a retail X520-DA2 installed in the T5600, and it boots with no problems. I am limited to copper CAT6a where this PC sits, else I would be using an X520-DA2 already.

What I have tried so far with the T5600 (troubleshooting):

---Updated to latest A15 BIOS.
---Cleared all BIOS settings (Set to Default).
---Upgraded the X540-T2's firmware in an Optiplex using "Version 18.3.6, A00" of "Intel NIC Family Version 18.3.0 Firmware for I350, I354, X520, X540, and X550 adapters"
---Disabling Onboard 1GB NIC
---Booting to DOS and running Intel's BootUtil, disabling NIC PXE: "bootutil –all –bootenable=disabled"
---Removing all RAM but one stick (16GB)
---Installing a Single 2GB RDIMM
---Removing One CPU
---Trying a different Graphics Card
---Trying every PCI-e slot.

None of this has worked so far. I am still stuck at the flashing cursor.

After all of this, I am not sure that this card is compatible at all with the T5600. Could anyone at Dell give me confirmation that this card will not work in this system, or maybe some more steps to try if you thing it SHOULD work? It works in almost every other system, but not the T5600, unfortunately. I know it is not listed on the compatibility list for 10GB adapters (Dell only lists Poweredges and 1 model or newer Precision Towers (T5610 and up)), but it really seems like it should work.

Thank you for your help!