Here are some more advice. Again, in points:
* From the processor specs I can easily say that a hardware upgrade would be
benefical for you since your current model was manufactured around late 2008,
while Intel started integrating their GPUs on the processor die with the
introduction of HD Graphics in 2010. Thus you need to rely on the graphic
card until you'll buy a new computer. If you'll buy a new Intel processor,
avoid models including the vPro/TXT privacy intrusive functionality.
* You need to decide whether you should buy the new components now, or rather
wait for the next generation Intel architecture codenamed Broadwell, that's
(according to Wikipedia) expected to be available in "the fourth quarter of
2014, with mass shipments in the first quarter of 2015". Although this isn't
important, it's interesting to see that Broadwell adds VP8 hardware decoding
support.
* There are many great free software games that may be interesting for you
(we can discuss this more broadly later). The most prevalent genre for which
there are more than enough games for are first-person shooters. The second
most common ones are strategy games. Some of the most graphically advanced
are Penumbra: Overture (2007), and Doom 3 BFG Edition (2012).
* Whether you will get rid of your current desktop or not, you should still
keep hold on the nVidia graphic card that might come handy in situations,
where the integrated graphics are not supported by the game/application you
want to run.
* From what I now read, the ethernet looks to be integrated on the mainboard,
so your computer might not contain any network card at all (this can be
confirmed only by opening the computer case, and listing the components by
manufacturer name, and model numbers).
* About the listed games, if not MMORPGs, they're all look to me proprietary.
And they require a pretty decent graphic card for smooth playablility, which
requires a hardware upgrade. For you to be able to run Windows games on
Trisquel, you will need Wine, respectively PlayOnLinux, or some kind of
emulator like Dolphin. Since the graphic drivers aren't on par in performance
with Windows, and these games will run non-natively, you need to expect
problems.
* Since you are going to play games, I expect you should also want quality
audio output from your computer for an immersive audio experience. If you do
care about this, I recommend you to buy an external DAC. I can recommend you
the Objective DAC (see section "Prices and Ordering") by NwAvGuy which
provides the best price/performance ratio among DACs currently on the market.
This is a great starting point in your audio chain (a quality amplifier,
headphone/speakers are also needed).
* If you're going to buy a new SSD, I recommend you to take the Samsung 840
series into consideration. This model while MLC based, provide comparable
endurance to the TLC based models, which means they are practicaly
indestructible in real-life use, no matter how much or intensively you will
gonna use/write to it. The review at Anandtech should provide you a good
insight into this.