Actually, you probably already have four primary partitions on your hard drive. HP have got in the habit setting up the computer with a partition for the bootloader, a recovery partition, a HP tools partitions, and the partition where they install Windows proper. All of these have been done as primary partitions, not leaving any options for creating new partitions since four is the maximum allowed on an MBR partition table.
The solution normally involves deleting one of the partitions and creating an extended partition which can in turn contain many more partitions. You can verify that this is the case by booting the Ubuntu LiveDVD and running Gparted. You can get more of an idea what to expect and how to fix it by looking at this previous question.
Alternatively you can install Ubuntu as a wubi install. This is not quite as good as installing alongside Windows because it runs off a virtual disk inside the Windows file system, however it will get you started until you are ready to make some changes to the hard drive. Before doing any installation or other changes to your hard it is vitally important that you make backups of all of your important data.