Your box will normally be able to boot up without a HDD. At the least, you should get a screen after the BIOS stating "Can't find startup disk" or something to that effect.
The things that would keep the PC from booting are:
A bad electrical connection - shorting out, or incorrectly plugged in
CPU fan not being attached to the correct headers
PSU is dead
PSU cables not properly plugged in
One more - this only happened to me once - plugged in the molex and the SATA power on an HDD and it wouldn't turn on.