Are you sure that you installed Ubuntu 12.04 and not Ubuntu 12.04.1 (Ubuntu 12.04 service pack 1)? If you downloaded it recently you will have downloaded and started with Ubuntu 12.04.1.
The reason for picking on the exact version of your installation medium is pretty simple and directly related to your problem installing Linux Mint 13:
When Ubuntu 12.04 was released end of April and Linux Mint 13 in May 2012 (Mint 13 being 90% Ubuntu plus a more polished and more user friendly user interface), they were both green bananas. The release notes explicitly mentioned particular hardware components which caused trouble during the installation.
The release notes for Ubuntu 12.04.1 do not mention any of those problems any longer, because the Ubuntu makers had fixed them all when they released Ubuntu12.04.1.
The problem with Linux Mint 13 is this: the installation ISO is still the May release of Mint 13. This means you start with a green banana version having all the bugs which have been fixed in Ubuntu 18.104.22.168. Provided you survive
the Mint 13 installation process (my machines all did) Mint 13 will pull round about 500 software updates thus lifting itself to the same bug-fixed state that Ubuntu 12.04.1 plus current updates will have today.
The symptom that you describe and which you kept on experiencing when trying to install Linux Mint 13 suggests that very likely your IBM notebook is affected by one of the compatibility problems which existed in the initial releases of Ubuntu 12.04 and Mint 13.
Linux Mint 13 release notes: May release notes
. See section "Known issues".
You may also like to look at the corresponding release notes for Ubuntu 12.04: Ubuntu 12.04
=> Ubuntu 12.04 Desktop
. See the section "Known issues" further down.In short words:
The trouble with the downloadable Linux Mint 13 installation medium is that it still represents the initial "green banana" state of Linux Mint 13, although most of the bugs have been fixed by now. This, however, will not help you, in case such an old bug prevents you from installing.
As the Mint makers are smart people the only reason for nor releasing bug-fixed Linux Mint 13 SP1 installation ISOs must be a lack of qualified people who have got the time to create these ISOs and distribute them to the servers.
With respect to your personal report, I would like to suggest to go through the old release notes and check whether your notebook might be affected by one of the reported known problems. - If you decide to stick with Ubuntu because you do not want to start all over from the scratch and spend more hours on making the Mint 13 installation work, then this is perfectly all right. Ubuntu 12.04.1 is a pretty stable operating system. And except for the Unity desktop there is nothing wrong with using it. (This is my personal point of view only.) For me it simply works.