You can absolutely have a computer without a CD drive... But how do you expect to install an OS on it?? Hopefully it can boot via USB stick or something so you can get the PC up and running.. hard drives don't come with an operating system on them.
But that is irrelevant, because if you cant POST, you can't boot from anything anyway!
Here is what I would do... remove absolutely EVERYTHING from the computer. Remove the hard drive, sound card, extra video card, etc (all you need is power supply, motherboard, processor, RAM, and video) and see if you can boot. Sometimes I remove the motherboard from the case, because I have had a few experiences where the motherboard was shorting against the case and not allowing it to boot.
Work a step at a time, verify each and every component. Make sure that the processor and RAM are fully seated and locked into place. Make sure the powersupply is fully plugged in (these days they have a large connector of 20 or 24 pins and a smaller connector of 4 or 6 pins)
If you still can't boot up, then its time to verify individual pieces... Grab a powersupply that you know is good, a video card that you know is good, etc. Swap every piece if you need to.
Good luck!