MacBook Pro won't boot, or boots slowly
The "invalid node structure" and "disk I/O" errors you see in verbose mode are both indicative of a failing hard drive.

The invalid node structure points to a problem with the data cataloging mechanism of the operating system, basically that system that keeps track of where all the data is stored.  One off reports of this aren't so bad but coupled with the issues you're seeing and the other error message I imagine it's a result of a failing drive.

The Disk I/O error pops up when the hard drive is inaccessible, either for a split second or several minutes.  This can usually be attributed to any of the following:


SATA port on the logic board going bad (not very likely)
Hard drive cable going bad (somewhat likely)
The hard drive itself failing or starting to fail (much more likely)


Because the disk is temporarily unavailable you often see system corruption (such as the invalid node structure error above) occur as a result.

So, what to do from here...


Definitely don't try to install a new operating system.  The process of doing so is one of the most taxing procedures a hard drive is likely to go through in normal use, on a failing drive it can stress it to the point of complete failure.
Backup your data if you haven't already.  If your Mac does manage to boot again I would strongly encourage you to copy whatever important data you might have (pictures, documents, etc) to a thumb drive or external hard drive.  If you're unable to do this then I would recommend checking with local AASPs (see two paragraphs down) to see about data recovery options.
Repair.  Depending on your comfort level working with computers you might attempt to repair your Mac yourself.  As I mentioned, the hard drive is the most likely culprit, iFixit has a guide that walks you through the process - MacBook Pro hard drive replacement. Almost any 2.5" SATA hard drive will work as a replacement.
If you prefer to have someone else repair it you can find Apple Authorized Service Providers (AASPs) and Apple retail stores using Apple's locate tool.  If your Mac is under warranty (you can check with this tool) then the repair would likely be covered by both Apple and/or an AASP so long as it wasn't a result of accidental damage.  If it's not covered then I would get a quote from each shop.


Hopefully that helps or at the very least gets you started.