Macbook Pro doesn't turn on...

Try holding down the power button. If that doesn't work, try resetting the SMC and PRAM. If neither of those work, then you can try pulling out your RAM modules and trying to turn it on with one in (try different slots, one of them definitely needs to be filled first, but I don't remember if it's the bottom or the top slot, only that it's DIMM0). … and if that fails, then you're probably stuck with taking it in.

I'll assume that you have backups. If so, try this:

Resetting the System Management Controller (SMC)

Should I do this if I don't have backups?

No. In that case your first concern is the safety your data, not booting. If you have another Mac with a FireWire port, boot the MBP in FireWire target mode and back it up from the other Mac. Otherwise you'll have to remove the internal drive and mount it in an external enclosure or dock. Do not write to the drive or try to boot from it before it has been backed up.

How to use and troubleshoot FireWire target disk mode

You can absolutely reset the SMC if you don't have a backup. It's a completely different chip, resetting the SMC will not touch your hard drive. If your computer isn't even getting to the gray screen, then you won't be able to start it in Target Disk Mode.

I can explain the RAM module stuff in more detail if it gets to that, but hopefully it won't, and even if it does, you may be better off letting Apple troubleshoot the RAM slots for you.

That's right. You must back up all your data by any means possible before you do anything else.

You can absolutely reset the SMC if you don't have a backup.

Wrong. Take risks with your own data, not the OP's. What is the point of resetting the SMC now? With the drive in an unknown state, he has to back up before attempting to boot or doing anything else. Resetting the SMC won't help with that.

As I've said, the System Management Controller is a separate chip. Apart from some freak power surge, which is just as likely to occur from any other activity as it is from resetting the SMC, there's no way that could damage your hard drive. If it posed any significant risk to the hard drive, then the SMC resetting article would mention backing up, but it doesn't.

Yes.

Remove the hard drive and mount it externally, as suggested above.

Because you probably don't have the tools to mount an internal hard drive externally just lying around (****, I don't), you can try just taking the hard drive out and then resetting the SMC. I'm not sure if that will work, but I think it's worth a try.