@tgdsilva Very sorry, I haven't been on the forum in quite some time and just saw your DM. In case this comes up in someone's search looking for an answer to this problem, there's only one thing that I can think of that could be the culprit; with the I340-T4 card installed, the computer can only see/address one of the two RAM slots on the Dell Optiplex 3020. Just to be clear, I was running the SFF (Small Form Factor) variant. When I had 2x4GB sticks installed, it would only see 4GB in the BIOS. If I only had one 4GB stick installed it would boot fine, so long as it was in the slot closest to the CPU. If I only had one stick installed and it was in the other slot, it wouldn't boot at all.
Full disclosure, I'm not certain which slot it was that worked, but the 3020 SFF only has two slots so it's one or the other. The 7020 and 9020 models both have 4 slots, but I never bothered to try to replicate the problem with one.
Hopefully this will help someone, if not the OP.
Oh, and here's an unrelated present; wanna boot & run this machine off an NVME? Here you go: https://www.tachytelic.net/2021/12/dell-optiplex-7020-nvme-ssd/