- You have downloaded the Server edition of Ubuntu
This does not come with a desktop environment and is not recommended unless you want to set up an application server. The installation process for the server edition is less user-friendly, and once installed it will boot to a plain text login with no GUI.
You are more likely to want the Desktop edition, and I suggest you download either the 11.10 or 12.04 image of this.
- Your laptop is configured to boot from the hard disk by default
You will need to either enter setup to reconfigure your BIOS to boot devices in a different order, or strike a particular key during POST. The messages that appear on screen will often inform you which key you need to push. F9, F10 and F2 are commonly used.
wubi.exe is used to install Ubuntu to what's called a "loopback file" - the file system is written to a file contained within your Windows partition. This is convenient for people who don't want to repartition your disk, but is probably not the best solution for you.
Since you have already had Ubuntu installed on your laptop, reinstalling over this pre-existing partition is probably your best bet. If you manage to boot the standard Desktop LiveCD, it should be reasonably clear which partition contains your current (broken) Ubuntu install.