Windows 7 isn't a problem. 6 GB is, however, and the i3 is not great. One other factor is the HDD -- slow spindle speed won't help, either.
It all comes down to what you want to do. If you're doing light tracking and mixing, it should be fine. If you're planning on huge multi-track sessions with lots of VSTs then you're not going to be happy at all.
+1One other factor is the HDD -- slow spindle speed won't help, either.
The i3 series, like most, has a huge range under the one name. "i3" alone tells us very little.
The range spans below and above the high end chips of yesteryear, meaning you could potentially 'upgrade' from core2quad to i3 and actually be taking a downward step.
I found a link to an x51 with Intel® Core™ i3-4130 though, which beats the pants off a q9550, for example.
If that's the chip in your machine, it'll be more than capable.
I used to have a q9550 setup with 8gb ram and never found the upper limit of what it could do in terms of audio.