CS 1.6 is not from 1998. Half-life was released in 1998. CS came out in 1999, but it was beta, and the graphics were very rudimentary. CS didn't even have a smoke grenade added until 2000, which was the strongest hit from a graphics standpoint that the game had. By the time 1.6 was released 3 years after CS was in beta, every weapon model had been upgraded, dozens of new guns and grenades had been added, and the maps had increased in both geometric and texture complexity. To claim that CS 1.6 is comparable to ANY games that were out in 1998 is flat out wrong.
That nitpicking aside, there's a couple steps to take. First, temperatures. Laptops are a different animal than desktops, and are much, much worse at dissipating heat. Heat buildup will force modern chips to reduce their speed as a method to prevent catastrophic overheat and failure. Find out what your temps are on ALL parts of your system; CPU and GFX are the primary ones to work about, but RAM, motherboard and hard drives can all cause clunky performance. Where is the laptop when you generally play? Do you put it on a desk or is it in your lap? Having the laptop on a hard service leaves the vents open; putting it on a soft surface like clothes or a bed can block ventillation and lead to overheating.
Second, drivers. You said everything was up to date. How did you install your drivers? Did you completely uninstall the old drivers before installing the new ones, or did you just go over the top? Make sure you've completely removed all old drivers, especially if you're switching to a third party driver.
Third, does this happen online only, or in LAN games as well? If you make a game locally, does it still occur? If it's only online, it's a network issue, such as a poor connection to a wireless network or inproper rate settings ingame.