Typically, the systematic approach to diagnosing a system is as follows:
Cables, connections, etc... You already did this.
I'd normally say test the PSU's voltage lines (+12, +5, +3.3, GND, +3.3vsb....), but I'd think if you had the means to do this, you already would have. At any rate, swap in a known good PSU, or verify that yours is good (don't use it in another computer, the potential to fry your buddy's computer is very real if your PSU is bad).
Unplug EVERYTHING except for the PSU and the CPU/heatsink. Yes, even the ram. power it up. If it beeps, the system is at least searching for the memory, narrowing the possability of a mobo failure. If you hear it beeping (I forgot that beep code), reinstall the RAM. The beep code should change to a "no video" code (long, short, short, short). If it does nothing with your ram, swap the ram with a known good stick. If that doesn't yield a "no video" beep code, I'd be willing to point my finger at the motherboard.
You'll need some good silver heatsink compound and possably a (plastic) scraper of some sort depending on weather or not you'll need to remove some cheap OEM Headpad transfers. DO NOT REUSE A HEATPAD!!! They're a one-time-only thing. That includes the aluminum ones, the soft "rubber" ones, and old heatsink compound.
Before condemning the motherboard, swap your CPU into a different computer. Don't put a good one into yours; your motherboard may fry it if the voltage regulator or related circuits are damaged. Obviously, if your buddy's computer won't post with your CPU in it (and making sure it's not overclocked; set everything to auto detect [if applicable] before the swap), you need to replace your CPU. But CPU's USUALLY don't just go bad (unless you're running a non-thermal protected CPU, aka: a Dinosaur) for no reason. As a general rule of thumb: if the CPU pops for no appearant reason (overclocking, loose heatsink), replace the mainboard, too. Also, sniffing around the large capacitors for a fish smell (if they're electrolytic) is a dead giveaway to a bad voltage regulator. Also, if you see pieces of brown paper (mica capacitors), buldging capacitor shells, or lifted cap shells, those give it away, too.
Things to note:
Some integrated systems (Dell, Compaq, some HP's) will NOT POST if they don't detect that a monitor is connected. You shouldn't have this problem.
The majority of fluke no-POSTs are caused by IRQ conflicts with the video card or other devices.
If a BIOS gets fried, they'll usually boot with a "Boot Block" BIOS. It just initializes the most basic inputs/outputs so you can reflash your BIOS with a boot diskette.
hope it helps!
CHayNZ