It doesn't power on at all? It could be your top case has failed. There are some pins you can touch on the logic board to boot it. You have to take the bottom off, plug it in, and follow these directions. If it comes on this way, your top case most likely needs replaced. I have seen this several times: http://www.insidemylaptop.com/turn-on-macbook-pro-laptop-without-power-button-locating-power-on-pads/ I'm assuming the charging cord glows green or orange and that the battery is charging right?
I've been able to run uBuntu 14 and uBuntu Mate on an 06 MacBook Pro A1150. Are you trying to do a dual system boot or just install Linux? Haven't tried the other versions you spoke of. With uBuntu, I used the alternate install disk and it worked just fine.
Your logic board is most likely failing. Sorry, I know that's not the answer you want to hear, but those models are famous for bulging capacitors. If you were to take the back off, I'm sure you see some (could try cleaning it with compressed air). You can replace them, if you know how to solder, otherwise you have to replace the logic board. I actually just ordered one for a guy who had the same exact problem. The board is about $50 on eBay. There's a guide on here to replace it if you want to DIY.
I guess it's possible your hard drive either got wiped or has failed. Which is uncommon on SSD drives. On that model, the cable that connects the hard drive to the logic board is famous for failing. I have replaced several. It's a lot cheaper to start there than replacing the hard drive. The "?" folder means there's no OS installed or no hard drive. If the ribbon has went bad, you will get that. I guess it's also possible the cable came disconnected from the logic board, could check that as well. Also you could take the 500GB drive out and put the SSD in there and see if you can get it to boot that way. If you do, then it's definitely the hard drive cable.
I'm pretty confident that's why it's not charging too. It's easier to just replace the DC-IN board on that model. It's about $15 on eBay for the part and the guide is of course on here. I have attempted to pull pins out, never had any success personally.
It could be a couple of things. Have you done these resets? If not, start there: https://support.apple.com/en-us/HT204063 https://support.apple.com/en-us/HT201295 If that doesn't fix it, I would take the bottom panel off (if you have the pentalobe screwdriver) and disconnect the battery and leave it unhooked for a while then reconnect everything and see what happens.
It could be the parts you replaced it with are bad. It could be the logic board has failed. Before going and buying other parts, try doing the SMC and PRAM resets on the MacBook. Sometimes when you change out parts you have to do the resets. https://support.apple.com/en-us/HT201295 https://support.apple.com/en-us/HT204063 Good job on trying it with an external monitor though. A lot of people leave that step out. I honestly don't think it's a logic board since it's working on an external.
I had a MacBook Pro once that had a similar problem. Doing the typical resets actually fixed it. The person I bought it from said it had a bad battery. When you plugged it in, nothing, no charging, light was green. Hit Shift+Control+Option+Power, let it sit for five seconds, with the cord plugged in, then reset the PRAM by holding down the power button til you see the light flash then when you hear the chime hold down Command+Option+P+R. If you do that right, it will restart, Do that three times. I saw you said you did the SMC reset. Sometimes you have to do all three resets. Might work, might not, on another one it did not. Could also remove the logic board and see if something is caked on the backside or near the battery or MagSafe port. I tear a lot of these apart and it can be several things. Sounds like your on the right track though!
The RAM upgrade would help. An SSD would be way better but of course the price is heftier. eBay has some good prices on SSDs though. You shouldn't be having too many problems currently on 4GB of RAM. Honestly, it sounds to me like it's time to format the hard drive and start with a fresh install of OS X. Which version are you running? You could back your pictures, etc. to a flash drive to save them before you do it. I refurbish Macs all the times and it's amazing the difference in performance you get from doing an erase and fresh install. Update (09/18/2015): Well you need to do a fresh install. If you have Yosemite, you have to create a USB boot drive or boot from the recovery partition, use disk utility, erase and fresh install. This is of course after you've backed up all your stuff to a USB drive or external hard drive. So here's the two methods: 1. Turn off the computer, hold down the option key when you hear the chime. Two hard drive icons will appear, the second one should be your recovery...
Did you hold down the power and home button at the same time? That should power it off. May need to go into DFU mode and connect to iTunes to un-brick it. Let me know if you need help with that.
If you’re replacing the board and the camera, make sure the part numbers match. There are different cameras out there that will attach to different boards but they will not work. To know if you mismatched one, your Mac will come on and the fans will run a full speed and the OS will be extremely slow. Also, the camera will not work. There are different ones you can use on different machines but I highly recommend replacing both the camera and the board to avoid the situation all together.
If you’re replacing the board and the camera, make sure the part numbers match. There are different cameras out there that will attach to different boards but they will not work. To know if you mismatched one, your Mac will come on and the fans will run a full speed and the OS will be extremely slow. Also, the camera will not work. There are different ones you can use on different machines but I highly recommend replacing both the camera and the board to avoid the situation all together.