I think I have bricked my MacBook Pro, what are my options to get it fixed?

Take it to an Apple Store (make an appointment first): they'll examine and diagnose it for you with no charge, and then tell you what they'd charge to fix it.

Doesn't cost you anything and if the price is too great or you'd rather fix it yourself (now that you know the problem) then you can simply decline the service. It's a no-pressure deal, and one of the primary reasons I recommend Macs.

You could try to drain the last energy out of the capacitors by removing the battery and the power cable, and then turn it on. Then try booting with a power cable again. If this doesn't help, there's not much you can do yourself.

I'd guess it's a motherboard issue, with the history of dodgy power supplies that's imho more likely than RAM giving out.

Removing the harddisk and saving your files is indeed an option, you could look at sata-docks like this one. That way you can just take the files off instead of having to deal with booting the os on the hard drive in another laptop if you get what I mean.

As to the price of the repair: I have no clue at all.

If you have a known-good power cable now, I'd try looking up "reset PMU macbook" and see if those instructions help at all. The PMU is a chip that governs the power management functions of the Mac, and if its settings get corrupt it could lead to a non-booting computer.

http://en.wikipedia.org/wiki/Power_Management_Unit

Another option you can do yourself it to reset the System Management Controller (SMC).

The list of power problems this can fix has enough overlap with your problems that it's likely worthwhile:

Power
The computer doesn't respond to the power button when pressed.
A portable Mac doesn't appear to respond properly when you close or open the lid.
The computer sleeps or shuts down unexpectedly.
The battery does not appear to be charging properly.
The MagSafe power adaptor LED doesn't appear to indicate the correct activity.