How were the gamers transported to the hospitals in Sword Art Online? Did the light novels (or manga) ever explain how the medical personnel were able to get the trapped gamers from their homes to the hospital without the NerveGear frying the gamers? From the anime's description, it should have been impossible, since the NerveGear would've killed anyone was physically disconnected from the game.
the NerveGear has a Battery

It also has a battery and internal memory to store data from the games. 30% of the NerveGear's weight is from its internal battery.

Source: NerveGear &gt; Appearance
according to the citation this was revealed in Volume 1 Chapter 3 of the Light Novel
Kirito also points this out in the first episode when Kayaba is addressing the players in the Town of Beginnings about the start of the Death Game

When Klein voiced his doubts on the situation, Kirito confirmed that the NerveGear's signals essentially functioned like microwaves, thus it was indeed plausible for them to cause lethal brain damage if the safeties were disabled. Kirito also explained the helmet had an internal battery, which rendered Klein's proposal to disconnect it from its power source meaningless.

Source: Sword Art Online Episode 01 &gt; Plot (7th Paragraph)

Klein:  What's that guy talking about he's gotta be nuts. Right Kirito?
Kirito: He's right that the transmitter's signals work just like microwaves.  If the safety were disabled it could fry a brain.
Klein:  Then, if we cut the power…
Kirito:  No, the NerveGear has an internal battery.

Source: Sword Art Online Episode 1 Animebreakdown.com
and as Kayaba mentions there had already been deaths due to people trying to remove the NerveGear despite his warnings. so either medical professional found out about the battery  or Kayaba had told them for the sake of making sure the players didn't just start dying off