As previously - you cannot put a 2.6 database onto a system which already has 2.7 installed.
1. Create a clone of your 2.6 site on your system2 - this includes copying the moodle code, the database and the moodledata folder. You will need to edit the config.php to point at the new locations for the database and moodledata folder. Given that your previous efforts have not worked - please make sure you are doing this with a completely fresh database etc. Do NOT try to duplicate the existing database from your system1 onto an existing moodle database wich may by now be a mix up between 2.6 and 2.7.
2. Go into the new clone version and check everything is working as expected. If you have any plugins, update them.
3. Remove the 2.6 code (except the config.php) and replace with the 2.7 code
4. Go back to the site and run through the upgrade process which should start automatically.
From Vivanath's question, it looks like you are doing both - migrating to a new server and upgrading. Follow the links he has given, but do them one at a time. Either migrate (clone) your site to your new server, make sure it works and then upgrade, OR upgrade in place, make sure it works and then migrate/clone. It seems like you are trying to do both processes at once.