Latency / Lagging question

O.K. I need a couple of things defined for me. when I am playing Half-life deathmatch and the game starts to lag, what causes this? Is it possible that the lag is coming from someone else dragging down the server, or possibly to much traffic on my ISP's servers? Also, during game play, how can I check my latency (lower is better, right?). When I do speed tests outside of gaming they always come back Awesome or Excellent. Why would they drop in game play? Does the setting of my monitor / graphics have anything to do with this?

Here are some specs that might help.

Intel Celeron CPU 2.40 GHz
Conextant D850 56K V.9x DFVc Modem
Intel(R) 82865G Graphics Controller [Display adapter]
DELL E773c [Monitor] (15.7"vis, s/n 641805690331, June 2005
Intel(R) PRO/100 VE Network Connection

Thanks for the help, please ask if you need more information.