Uh-oh dear VMware.... I don't know where you're heading, but I can smell it's Microsoft route - path of self destruction.
First there was an issue wtih Realtek nics. After 5.1 no more drivers for Realtek nics. OK, no 'enterprise' targeted chips so we said fine, we could live with 5.1->upgrade and preserve drivers->5.5.
But now I got an big black machine with i350 T4 chip (quad port). And yet I cannot install the damn thing! NO ADAPTERS FOUND!
I relocated the NIC onto my whitebox machine (which has 3x Realtek nics and working just fine with 5.1 upgraded to 5.5 U2), and guess what - lspci shows adapters just fine but ESXi 5.5 U2 is unable to load drivers for those i.e. NOT even showing on esxcli network nic list! I've tried various versions of igb drivers, both older and the latest ones, but still was unable to get it working!
Big big shame on you VMware. This card costs 400+ $ (300+ EUR) and you state on your HCL it's suppose to be working out of the box but yet it doesn't work on latest and STABLE Hypervisor software from your factory (5.5 U2)?!
Friendly advice: take a breath to remember that Hypervisor ESXi is your flagship software, and that this game of thrones with NIC drivers can't be good for ESXi future!
Since I work for a company which is 100% on ESXi (16 ESXi hosts), I will ASAP initiate procedure evaluating XenServer instead of VMware. TCO with Xen is better anyway. When you realize that more and more customers are heading that route, I'm afraid it's gonna be too late... but that's how it goes in IT business!
Shame shame shame, all I can say on this!!!