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Boot up a live cd or usb, and go into try ubuntu mode. Open file explorer, and see if you can find your Ubuntu partition. If you can't find it, open a terminal by pressing Ctr-Alt-T on your keyboard and type in:
sudo su
gparted
In the window that opens up, find your hard drive, and note its /dev/sdX. The X here is for example, you have to replace it with whatever lowercase letter you got when you found the drive in gparted. Then, in the terminal, run this:
mkdir /media/ubuntu/Ubuntu
mount /dev/sdX1 /media/ubuntu/Ubuntu
nautilus /media/ubuntu/Ubuntu
Remember to replace X with the appropriate letter.
These commands mount your Ubuntu partition so you can view the files. Now you should have a file explorer window open with the root directory of your Ubuntu installation open. Open the folder home, and go into your user folder. Now you can plug in a backup drive and copy all the files over. Then when you install Ubuntu again, you can copy the files over.
If you don't see a home directory in the folder you opened, then probably /home was located on /dev/sdX6. In that case, can mount it by typing the same commands above but replacing /dev/sdX1 with /dev/sdX6 and /media/ubuntu/Ubuntu with /media/ubuntu/Home. It's always good to make backups.
If /dev/sdX6 is the home partition, you can do a reinstall without wiping it. Start the install by clicking the Start Install icon on the Desktop, and once you get to the Something Else screen designate /home to be on /dev/sdX6. Just don't format the partition! If you do, you will lose all your files.
But first, what's wrong with your computer? Does it turn on? What do you see? Do you get an error message? Do you get to the grub menu? Do you get to the startup screen?
Most of the time, you can repair the installation without having to reinstall. To help us help you better, could you edit your question or reply to this answer explaining exactly what the problem is.
