I am new to all of this and I managed to get a Raspberry Pi 2011.12. Since I have not attempted to build anything before, I am already hitting a wall. I have tried looking things up on the web, but it suggests to buy a lot of things. I understand it is unlikely that you have all the products yourself, but I would like to utilise what I already have and perhaps use that to build something later on again. Currently, I have an old Dell PC and the Raspberry circuit itself. Any suggestions are much appreciated. I am excited to know what my first project could be. Thanks a ton.
You can't build much without the proper building blocks :)
However, the Pi is a good platform to learn programming, especially Python and C. One thing you could build would be something to do with networking. For example, there are utilities (nmap is one of them) that allow you to discover other devices on your network, with their IP, their MAC address and their hostname. You could write a script that periodically checks for new devices on the network (or devices that leave the network, or both) and send you an email about it. This is useful to determine if and when a device stops responding and may need a reboot.
There are one or two things you might play about with using minimal hardware.
Kodi is one of the most popular media centre programs out there. It plays pretty much everything, and it has a fairly huge array of community built add-ons that allow streaming of radio, TV and movies. OpenELEC is a variant of Kodi which has been somewhat optimised for tiny computers like Raspberry Pis. I've run a copy of OpenELEC from a Pi 2 hooked up to my main TV for the last few years, and it's great. They have a decent write-up on the setup/installation process on their wiki page here.
Makezine have a good tutorial on turning your Pi into a short range FM transmitter here. The sum total of the equipment required is a length of wire that you can connect (you might get away with wrapping a pin if you don't have a soldering iron or pin headers) to a GPIO pin. Make have provided a pre-built image file accompanying the tutorial, which contains a modified version of the venerable PiFM application by Oliver Mattos and Oskar Weigl. If you can get this project up and running you should be able to transmit audio from your Pi via the antenna to any nearby FM radios.