I don't know why anyone would want to do this in this day and age, but I had a situation where I had to do it, so I'll just write it down here for anyone else who needs this info.

Obtain the installer from the ESXi server

Ah, and here you already will run into a problem. The webpage won't open! At least, it doesn't on most Windows Server 2003 systems, because of an outdated SSL ciphersuite. But this can be fixed if you read on. The link in the next chapter will update the ciphersuite in the operating system and this will also fix the ability for your browser to open the webpage of the ESXi server.

Update the SSL ciphersuite on Windows

You will see this error message when trying to connect from a Windows Server 2003 machine:
[code]vSphere Client could not connect to "esxi.server.com".
An unknown connection error occurred. (The client could not send a complete request to the server. (The underyling connection was closed: An unexpected error occurred on a send.))[/code]

The reason you're seeing this message is because the server uses SSL encryption with ciphers that your client doesn't understand. The reason it doesn't is because it relies on the operating system's list of available ciphers. And the operating system is old and doesn't have the modern ciphers. So you need to update your ciphersuite. There is no 'Windows Update' for this, but there is a hotfix for this. You can obtain it from Microsoft here, after you select the correct version for your system language and architecture, and receive their hotfix via email:

https://support.microsoft.com/en-us/kb/948963

This update does require a reboot. It offers the option to postpone the restart but when I did that, and rebooted later, it wouldn't work. A fluke, maybe, but it's best to just run the update and then restart when it tells you to.

Install on a domain controller

You will see this error message when you try to install on a domain controller:

vsphere Client requires Windows XP SP2 or later.
vSphere Client cannot be installed on a Domain Controller.

Well, okay, but I want to do that anyway. You may use the flag /VSKIP_OS_CHECKS="1" to bypass this check. It will bypass the operating system check and the thing will just install and work perfectly. Please note that this goes against VMWare's recommendations, but then I figure if you're reading this and still using Windows Server 2003, you're probably already doing worse things.

VMware-viclient-all-5.5.0-12816505.5.exe /VSKIP_OS_CHECKS="1"