I was wondering if my computer is good for gaming?

I currently have a Windows XP, Lenovo, as a hand me down.
My system information is
Pentium (R) Dual Core
T4200 @ 2.00 GHz
1.99Ghz, 1.96GB of Ram.

No, it is not fit for moderns games with latest OS.
Can use obsolete OS like winXP and low resource hungry games like CS1.6, nfs mostwanted or better say games released prior to 2009 or so.

No. It is below than average for playing games.

You should a better CPU with at least following configuration if you want to modern games:
- 16GB Of RAM.
- 1 GB of Nvidia Graphics card especially from the series 500, 600 or 700.
- 4th Gen Core i5 processor.