I do believe it makes a difference in upgrading to jump major releases.
Did you review Upgrading_WordPress_Extended
Before you started?
Detailed Upgrade Instructions for 1.5.x, and versions 2.0 - 2.6.5, to 3.4.1
The following are the instructions that explain the above steps in more detail. Please read all of the instructions before starting.
If you plan on upgrading across more than two major releases, please consider upgrading incrementally to avoid potential conflicts. For example, if you plan on upgrading from 2.5 to 3.4.1, upgrade to 2.7 first, followed by 2.9, and finally 3.4.1. Essential, it's okay to skip one release, but never skip TWO when upgrading.
You say you have a back up of the 2.6 files did you also take a database backup? Without that you don't really have your content.
And you should back up what you have now in case you didn't keep your database.
Also check these forums, the last few days I have seen several people with a very similar problem, and somehow they are all related to something happening on their hosts server (Blue Host I believe).
Have your urls always been numerical? I still think you should talk with your hosts.
I have also read on these forums of several people who upgraded to 3.4 who had problems, did down grade successfully. Perhaps that is what you need to do, then to incremental upgrades, with total back ups in between, and testing plugins and themes, so you will see where the issue starts. Sorry I don't have a better idea.