sure you can, to only a certain degree. If you are familiar, you can do a masking on the trees and correctly exposed parts, then use Curves, Adjustments, color balance, layer types etc, to bring out the mountains clearly
I'm no PS expert, so you will need to try out. Use the adjustment layers for easy manipulation.
With my limited knowleage of ps, this is the most detail i can get out of that rock in terms of tweaking the photo haha.
to look exactly the other photo u posted i think would require some major reworking (e.g. replacing of color?) , also not sure can get the same look or not.
Also can tell that the photos were taken at different time of the day judging from the shadows.So u might wan to try taking the easier way out, by taking the photo when the sun is actually shining on that surface of the rock the next time (if there is a next time).
Here's my attempt to make elcapitan less blue as requested by original poster.
I kept the trees and foreground pretty much as it is. However I thought the sky should have a little more color. Hard to say if this works better or not because El Capitan is now somewhat monochrome and not much of earth tones in it.
I doubt you can get close to the image you googled as both your shot and the googled one were taken at different times of the day. The sunlight in yours is coming from practically the opposite direction of the sunlight in the googled image. The rock face in your image is in the shadow so you already lose out in detail and colour which most likely cannot be fixed in PS.
maybe. If it's shot in RAW, the chances of correcting the White Balance is there. you can also mask the blue tint away. then multi exposure can be developed in JPG and then combined with photomatix. playing around with the tone, you may be able to bring the elcapitan back to a brighter color.
Just follow in the HDR thread...play around with your cam. this HDR thing is pretty interesting. BTW, even a P&S can be used for HDR as long as there is a EV bracketing, you can shoot and compose in HDR.