Sometimes we can't use VMware Hardware Compatibility Guide-verified components, but still need a working VMware...
virtualization infrastructure. There are two ways to research a component's ESXi compatibility.
The VMware HCG lists hardware for which drivers exist in the VMware hypervisor. It also ensures that hardware stacks are known good, meaning that component A and B can work together with component C within a VMware environment without causing problems. It exists to benefit VMware, third-party vendors and VMware's user base.
Hardware vendors expend a fair amount of time and money to get a product HCG-certified. Not every manufacturer chooses to do it, and certainly not for every product in their portfolios. Even if a manufacturer does participate, newly released equipment could take months to certify.
When you have hardware that VMware doesn't list on its HCG, there are two ways to verify that the ESXi infrastructure will still work. Start with the easy route: Check your components against the VMware community's list of hardware known to work with various versions of VMware products. The user ratings here will give you a general idea of what to expect.
If you find no ESXi compatibility information in the community list, its time to dive into a long, hard process of identifying each of the components of your server and then determining if drivers exist for them within VMware's ESXi hypervisor. This can be fairly straightforward or miserably complex, depending on the documentation trail.
Start with the CPU. If it doesn't have hardware virtualization, stop. In today's world, without hardware virtualization, it really doesn't matter if any of the other components are supported.
Check your motherboard. Not all motherboards support CPUs with hardware virtualization. You can investigate this by looking into the southbridge; motherboard incompatibility almost always stems from an issue with the southbridge, the core logic chipset on a motherboard that typically handles slower tasks.
Motherboard makers have to buy their chipsets and other subcomponents from a pool of suppliers at roughly the same time, and they often put together very similar combinations. Because of this, motherboard product lines are generally very similar, so check the compatibility lists for motherboards that are like yours, but by a different maker. For example, if an ASUS board with a Q77 chipset isn't listed, look for a similar offering from Micro-Star International Co Ltd. (MSI) or Giga-byte Technology Co Ltd. If the TYAN board you want to use isn't listed, check for a similar one from Supermicro.
Cross-checking between vendors works for other components as well. For example, if your RAID controller uses an LSI1078E chip but isn't listed on VMware's HCG, check if VMware ESXi is compatible with other 1078E-based RAID controllers. If it is, chances are excellent that the unsupported RAID controller will work.
A word of caution
There's a distinction between "working" and "working the way you expect it to" when you source non-HCG components. Consider PMC Inc's Adaptec 3805 RAID controllers. ESXi will see disks presented to the OS by these controllers, but it cannot access any more information. You cannot check on the health of individual disks or even get an alert when an array fails.
Spend more time on research when you stray from the VMware HCG. Often, Google searches will tell you what issues others had with a particular piece of hardware and what driver VMware uses to support it.
Driver quality is important. The NVIDIA nForce chipset-integrated network interface cards use the open-source Linux forcedeth driver in VMware. It's common for VMware to exploit open-source drivers in ESXi, via an emulation layer called vmklinux. Here's the problem: nForce NICs in combination with the forcedeth driver are pretty awful. Taking the nForce Professional 2000 as an example, you will be lucky to get 200 megabit out of a NIC that supposedly offers gigabit performance.
VMware is pretty open about the changes it makes to the drivers in updates and new versions of its software, if you're willing to read the release notes. Even so, individually verifying your components as ESXi-compatible will likely be an arduous task. The information is out there -- it is only a question of how much time you have available to find it.