In Episode 2 they aren't linked. Perhaps both are integrated into the HEV suit: the sprinting could actually be the suit artificially increasing the speed of Gordon Freeman by powering his legs.
Or maybe Gordon needs the suit to run because he's broken his legs like a million times.
When in Half Life 2, notice how when using the sprint, flashlight, and/or the oxygen function, the words "AUX POWER" appear. This is short for Auxillary Power, which is likely the HEV suit's own power system. (Not to be confused with suit power, which is the suit's main power system) The first answer is correct; Both systems, along with the oxygen, are connected to the suit's AUX POWER. However, commentary in Episode 2 states that play testers often complained about running out of energy when running from the guardian in the tunnels. Therefore, they decided to add a spearate flashlight that Gordon "finds" in the train wreck at the beginning. Players then assume that the built in flashlight on the HEV suit was damaged during the crash.