Any layer 2 hardware allows net boot - hub or switch. Its just an ethernet broadcast the first time. (Direct for renewals) actually you can't stop it on a hub, potentially you could filter out the packets with a manageable switch ... So you are fine there.
Definetly the Dell should be able to net boot. Strange thing is, if it has the option as F12, then not only should it work, but it should appear in your boot sequence in BIOS. You may have to "enable" it in the boot saequence before it appears. BTW it will be described as PXE, not network boot, in the BIOS.
Also, look at your core's DHCP config - remove any leases that are there already for that PC by MAC address and try again...