Depending upon the age of your computer, you may have a processor that does not support the latest versions of Ubuntu.
Try downloading Ubuntu 10.04 LTS and burning it onto a CD. Make sure you burn it as an ISO image, and not simply as a file or it will not boot.
After 10.04 LTS, Ubuntu changed the kernel, and the later kernel will not run on older processors. Ubuntu also has problems booting on some machines, and requires command line options to be used in the boot process to get it to work. Unfortunately, I do not have a list of those options available, but the boot help when you boot from the CD may give you some clues as to what you might need.
Ubuntu 10.04 LTS is still available from the www.ubuntu.com.
If your computer will boot and run from the CD (without installing it), this will give you an indication that all is well. While it is running from the CD, it will provide an option on the desktop to install it onto the hard disk.
There is also a version on the web site that installs as a Windows application. Generally, this can run a bit slower than a full native install, and it may not offer all the features of the native version. You will have to try it to find out. I have not tried this yet.
Good Luck.
EDIT: I have now tried the installation as a Windows application. It looks like it only allows the installation of the latest version (currently 11.10), but it did install and run successfully on a laptop that had previously had problems installing the most recent versions. Unlike native installations, it did not need to have a CD burned from an image file, and did not require its own separate file systems on the hard disk. Instead, it used up about 5 GB of disk space on a Windows partition (I chose which partition it would use). Also, unlike the previous Ubuntu installations I have tried, it did not set up its own boot menu system, but added the Ubuntu option to the normal Windows boot menu. (If you have the timeout in your C:\boot.ini file set to 0, you will probably want to change this to a higher figure - I use 3. With a timeout of 0, it will boot into your default operating system without giving you time to choose a different one.)