First, the 80GB rating is deceptive. The 80GB rating assumes a conversion rate of 1000MB to 1 GB. In reality, this conversion should be 1024 MB to 1 GB. So, the actual hard drive space is going to be slightly less than 80GB.
Next, let's take a look at your partitions. You've got a system partition (C) which is 51.23GB in size. It looks like your manufacturer created a second partition (D), and allocated the 17.1 GB it contains for Backups. So, we're looking at 68.33 GB between those two drives.
Next, you've got two other partitions listed. This is where some undefined variables come into play. Where did you buy the computer from and what kind of hardware is in it? The smaller of the two partitions is labeled EISA Configuration. Someone else here will correct me if I'm flat out wrong, but my best google searching reports that this is used to configure devices on an ISA bus. This confuses me a bit, since you said this is a new computer, yet I was under the impression that ISA was pretty much dead in new pc's.
The larger of the two partitions is labeled Unknown, which provides a mystery in itself. Best guess says that this could be a recovery partition, created by the manufacturer, to be used to roll the computer back to factory defaults.
The bottom line: Your 80 GB drive is broken up into pieces, like a pie. Each of the entries on the table you posted represents a piece of that 80 GB. To find the total space on your physical hard drive, you need to add up those pieces. I didn't do the math exactly, but it looks like the total of those pieces is somewhere in the ballpark of 75 GB.
