I am unsure just what your trouble is at this point. It appears that your system is not completing the boot up since you do not get to a point where you can switch to a console log in screen.
If you have your /home directory on its own partition a fresh installation will not wipe out all your user accounts data because that partition (/home) is not usually formatted (unless you specifically format the partition).
If you have Mandriva installed on a single partition mounted at the root (/) of the file system, you should get a live! CD image, burn it to a disk, boot your computer from it, then mount your partition and copy any files you do not want to lose to a CD or DVD. This will work only if you have a CD or DVD burner.
If you do not have a CD or DVD burner, you should be able to get a USB flash drive suitable for this purpose. I got an 8 GB flash drive here for about $20.00 (US funds) recently and I saw a 16 GB drive for about $40.00. You will need one drive to which you will install Mandriva One and another to save your files on, so look for one large enough for a CD image (about 700 MB or larger will do) and another of sufficient size for your data files. All the Mandriva 2009.1 (Spring) iso image files are hybrid iso's that can be dumped onto a USB flash drive using dd in Linux or rawrite in Windows. You can also use rawritewin in Windows. These two Windows based utilities can be found in the ~/2009.1/i586/dosutils/ or ~/2009.1/x86_64/dosutils/ directory on the Mandriva ftp mirror of your choice.
In Linux, copy the iso image using dd. This example assumes the following:
The Mandriva One iso image file is in the user's home directory.
The image file is being copied from the user's home directory.
The USB flash drive is recognized as /dev/sdb
You will use the English version of Mandriva One with the KDE Desktop environment
In a terminal window (as root) execute the following command to copy the iso image to the USB drive:
dd if= /home/$USER/mandriva-linux-one-2009.1-KDE4-europe1-americas-cdrom-i586.iso of=/dev/sdb bs=8M
Notes: The above command can be used as is if you meet the criteria specified above.
$USER can be replaced with the user's directory name.
If you will be using a different Mandriva One CD image, replace
mandriva-linux-one-2009.1-KDE4-europe1-americas-cdrom-i586.iso with the actual file name.
/dev/sdb should be replaced with the actual device node of your USB flash drive.
If this process is to be attempted from Windows, I believe that rawritewin (or rawrite)
will work as expected, but if they do not, you can get dd for Windows at
http://www.chrysocome.net/dd
HTH,