mikemcsw -- Texiwill is correct. With a PATA drive only you'll be able to install and boot into ESX but a PATA drive won't be able to store VMs. However...
Option 1: I looked at a Dell GX270 Mini-tower unit today on your behalf to check the built-in SATA controller. It's an Intel ICH5 and ESX will see it as an 82801EB SATA controller and use that SATA controller with an attached SATA 150 hard drive to store VMs on it if you attach a SATA I (SATA 150) drive to the GX270 SATA port. That would give you a self-contained GX270 machine that would run ESX 3.5 and also host the VMs.
Here are a few other options to consider if you want to go further:
Option 2: If you have Win2003 Server running on your other home computer (or if you have VMware Workstation on that computer and run Win2003 in a VM) you could download Microsoft's free Services For Unix (SFU) feature and make that Win2003 VM into an NFS server where your Dell GX270 ESX host could store VMs. This would also allow you to have shared storage in the event you get a 2nd ESX host and want to use a trial license for VMotion and learn the details of DRS (Distributed Resource Scheduler) and VMware HA (High Availability). This wouldn't be a screaming fast setup but it would get to going and allow you to learn the advanced features of ESX.
Option 3: If you're a Linux prone person you could just load up a separate computer with Fedora or CentOS (or put them in a VM on your other home computer running under VMware Workstation) and create an NFS share on that Fedora/CentOS box. Your Dell GX270 ESX machine will use that NFS space as a place to put VMs on it.
Option 4: xtravirt.com has written directions on how to rig up a separate iSCSI server (or an iSCSI server within a VM) where your ESX VMs can also be located (in addition to the NFS space option described in Option 2 and 3 above).
Datto