Can't Power Up 2006 G5 Mac Pro

That is not a G5 Power Mac if it is running Snow Leopard. Snow Leopard only runs on a Mac Pro which is not a G5 but an Intel Mac.

I would take it in for service as it sounds like the power supply may have gone, although you may wish to check that that the power cord is plugged in on both ends.

Flashing lights usually mean something.

Make a note of the pattern, they normally repeat giving a specific pattern for specific faults. It can give you something concrete to search for in Apple's manuals & Mac repair sites.

Remove all peripherals & retry booting.

You can do all the regular resets & try booting from some other media (an OS installer disk or a backup etc)…

How to Reset NVRAM on your Mac - Apple Support

Using Apple Hardware Test - Apple Support

Resetting the System Management Controller (SMC) on your Mac - Apple Support

Assuming you can boot in some way…

Try safe mode if your Mac doesn't finish starting up - Apple Support

Limited graphics performance in OS X recovery or safe mode - Apple Support

http://www.kelleycomputing.net/rember/ (3rd party RAM test).

The Mac may also have diagnostic LED's inside, see if any are lit up when it fails to startup. You may need a bright light to see what text is printed next to the LED's (if any is visible).

I'd also leave it rest with no power connected overnight, it may reset any components that are failing/ faulty. Removing the PRAM battery will cause the PRAM to reset if left without power.

Also don't forget to check the PRAM battery voltage (or change it if is old). Clean out any dust bunnies if you are familiar with working on computers.

Double check the RAM too, it can be easy to remove & replace it incorrectly when a computer is non-booting. Perhaps try 1/2 the modules as a test.

The power light blinking in a deliberate way usually indicates "not enough working RAM to start up".

The RAM must be installed in pairs in adjacent slots on the same riser-card (except for the case where you have exactly TWO modules).

The power light is under firmware control, so even if nothing else works, your Mac Pro "is alive".

The coin cell PRAM Backup battery is a nominal 3 Volts when new, tested in hand (not in circuit, where you will read the "always-on" power supply if the AC cord is present).

"Almost as good" batteries with a slightly different number (CR 2032 instead of the regulation BR 2032) are used in car key fobs and garage door openers. They have a narrower temperature range and may not last quite as long, but are more widely available.

Another rare problem can be caused by the NorthBridge chip losing one or both of its plastic mounting pins. This will make the chip heatsink "wiggly", and often cause wacky memory problems. You may be able to check it for snug without dis-assembly.

I don't know what model we are working with here. It may not fail like this with a bad PRAM battery.

Older Macs have appeared to be dead like this on occasion, but sprang into life when a new PRAM battery was fitted, so I figured it would be a reasonable thing to check.

You can do an NVRAM reset after replacing the battery but it may be pointless – removing the battery with no power connected to the Mac will cause it to lose the PRAM settings (a.k.a. NVRAM).

I'm not at all convinced that the battery is at fault. Please provide more info…

What model is this?

Does it have additional third party hardware (graphics cards or other internal additions).

What it the pattern to the LED? Does it pulse at all? Is the power LED blinking on the Mac, the monitor or both?

Are there any internal LED's lit up? - It is safe to try a boot without the side door as a quick test, it may activate the fans & a warning LED in that mode.

The plastic clips can fail at any point, it doesn't take much movement, especially when you consider that the Mac was probably warm when it died (e.g. heat can cause enough movement to make a heat sink fail to work as intended).

Intel-based Mac Power On Self Test RAM error codes - Apple Support

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