In most cases, deleting a partition doesn't actually destroy filesystem data; it just deletes the pointers to the data. (Partition table data consists mostly of pointers to where filesystems start and stop.) Thus, when you deleted a partition and re-created it in exactly the same way, the original filesystem data became available again.
Instead of trying to delete and re-create the partition, you should be able to use the "Something Else" screens to re-install over the existing system. Be sure to select the check box to "format" the Ubuntu root (/) filesystem. This will quickly delete all the important filesystem data structures. Alternatively, you could use GParted or text-mode tools like mkfs to wipe the original Ubuntu 14.04 partition before launching Ubiquity (the Ubuntu installer). You'd need to boot into the installation medium's "try before installing" mode or use some other emergency tool in order to do this, though.
As a side note, I recommend taking this opportunity to upgrade to Ubuntu 16.04. Although 14.04 is still supported, it's over halfway through its supported period; it will enter unsupported status in less than two years. Ubuntu 16.04 also offers a number of updates and improvements over 14.04.
