Are you multiplaying with these two machines because if you are, especially if your dad's machine is hosting the games it will slow up significantly.
It's this machine that needs more attention than yours because no matter how fast your machine is it will be held up by the slowest machine
and as his board only supports DDR2 memory, the motherboard is your start point, then get 8GB DDR3 memory for it and a new Processor.
Although of course you could build a new machine for yourself, and upgrade your existing machine with a AMD Phenom II X4 955, which i think is a better processor
than the AMD 1055T.
Does AM3+ Sockets Fits on my motherboards?
No it has a AM3 socket.
If you have any other proccessors that would be AMD and fit my motherboard please suggest them! But i would like to really have it to improve my computer before i would buy it.
You need to consider what you want to use the computer for when choosing a Processor, is it for general use, gaming or a specific multithreading environment and how much you want to spend.
For gaming Core i5-3570K can be overclocked easily to 4.5GHz+, or there's the Core i7 3770K.
For AMD there's the FX-8150 which overclocks at 4.7GHz (you'll need a Fx-Board for that), the AMD Phenom II X4 955 (Uses the AM3 socket) offers good value for money especially at stock speeds for general use.
So let us suppose you want the i5, you'll need a motherboard, something decent like the Asus Maximus V gene series of boards for the LGA1155 processors.
You'll need a Power supply that is over 1000 watts, Liquid cooling like the Corsair H100 and a new case to get the most out of the cpu overclocking capabilities
and lets not forget the graphics card, something like one of the GTX 500-series maybe to really make a difference.