If your PC does not POST beep straight away you have one of two issues, the power supply is not delivering enough voltage in the right places to boot the mainboard or the mainboard is struggling to boot itself or a component plugged into it. POST is power on self test, the single beep just means OK.
it is likely that it is a board issue, I would seriously consider taking it to a professional (or return under warranty if applicable) as it is going to be difficult to diagnose without having plenty of spare parts and diagnostic software to check each part.
I am a technician so I am used to this sort of diagnostics but it is difficult for many non-techies to pluck up the courage to open up their PC, but if you are confident about playing with the internals of your PC try the following.
Unplug the PC from the mains, take off the left side panel (Looking from the front) ground yourself against the PC chassis before touching anything on the inside (just touch the frame with both hands to dissipate any static electricity)
Remove all the add in cards one at a time and replace in the same slots, do this for the memory modules as well.
Then unplug and reconnect all the power cables and data ribbons to all the hardware, so your hard drive, DVD, Floppy disc drives everything on the mainboard, and then plug in to the mains electric and restart. Is this any better, if so it was a loose connection and hopefully problem solved.
No change? Unplug from the mains again and then unplug everything (HD,DVD, FDD etc) on the inside except the mainboard power cables (so NOT the big 20/24 cable block and the smaller 4 cable block near the processor fan or it wont start at all) unplug the usb and front panel Audio cables near the bottom of the mainboard (note which goes where) but dont unplug the cable for the power, reset, HD or Power LEDs and do not unplug the fan for the processor (do unplug all the others). Reboot, and what you are testing for is to see if it beeps more or less straight away. Hopefully it will, if not then you have narrowed it down to Power, Mainboard, Processor or Memory. All of these you are better to seek professional advice for.
If it beeps normally connect one device at a time, until the beep at boot is delayed and that is the faulty component.
The hassle comes when you get no change at all, then you are back to the power supply, CPU, Memory or the mainboard itself. The mainboard you can try upgrading to a newer version of the BIOS if one is available but you should be aware that if it goes wrong your machine may not be bootable without a reloading either the original BIOS version or another new one. Obviously if this is the only PC you have in the house then you cant download a new version as your only PC is not working. If you have more than one memory module boot with only one installed at a time until all have been tested individually and there is either no change or one or more seems to slow the POST beep down.
Another very simple thing just occured to me, is there a CD or DVD in the drive when it boots? Sometimes having a disk in the drive will stop it from booting to Windows straight away but usually it will beep for the POST as normal.