Ok!
And thanks!
This remind me of an old bug from joomla... SO, i will recommend you to check database if updated (in admin joomla extension manager).
Secundly, will test to install the update archive of Joomla 2.5 from 2.5.X to 2.5.27 to be sure all new files are the good ones in Joomla core.
About iCagenda, you will have to delete the wrong database entries. this could be done in manual, in #__extensions (where you will found com_icagenda)
Then check too in #__assets, #__schemas and #__menu, if no com_icagenda entry.
More info here:
stackoverflow.com/a/22409034
I think an issue happened when first install, and this one was broken. So other installation weren't working properly.
This is a reason i suspect a problem in Joomla core install...
Best Regards,
Cyril