> how do you change the bios battery in a dell GX1?

GX1 covers a lot of ground. It appears that you could be
talking either a desktop or a tower ... either way ... you're
looking for a CR2032 coin cell ... just about anywhere
you've seen a display of batteries should have this one
in the mix ... drugstore, hardware, camera, etc. (though
will note that the big grocery stores here don't stock
them) Buying the battery first will give you the big
clue as to what you're looking for when you take the
case off of the computer. If you need a tool (very
rare) it would be a small phillips type, but most are
just a bit of spring metal to hold the battery in place.

> does the battery recharge itself?

Although super-capacitors and ni-cads have been used in
a few designs, the general answer is no. In fact, the
standard 2032 button-cell type tends to explode if one
attempts to charge it.

> if so, does it only charge when the computer is turned on,
> or is there some sort of bypass feed that lets it trickle charge
> when the computer is off?

More likely is a diode to keep the power supply voltages
away from the battery .. only letting battery voltage 'appear'
when the power supply goes away.

> in other words, if a computer is off for a long time but
> plugged in, will the battery still be up?

In the olden days, AT design and below, if the computer
was turned off, battery was used to keep the CMOS and
clock running. On the ATX designs and newer, the power
supply doesn't shut fully off unless unplugged from the wall,
such that the battery doesn't come into play unless the unit
is physically unplugged from the wall (or power goes out)
Easy way to tell the difference ... AT class and older was a
mechanical on/off switch ... ATX stuff is a momentary
contact switch that completes a circuit while you push it ...
specifically tirning the computer off -- AT switch snaps and
computer is off .. ATX you usually have to hold the switch
in for 3 to 5 seconds and then eventually shuts the computer
down (again, sitting there in a reduced power state waiting for
the next push to jump back to the 'on' mode.)

> do you leave the machine running while you swap out
> the battery?

Not a good idea. Live power, little tiny screws or bits
of spring steel on the battery holder, which is not
necessarily out in the open to begin with. Odds are
that a drive cable or two will either be in the way
or at least partially pulled while fiddling around with
the internals.

> I'm guessing you would, or else bye bye data...?

Typically, one wouldn't be asking about the motherboard
battery unless there was an issue with data being lost.
Typically, the clock is wrong, the date shows up as 1980
on a Windows type computer, hard drives may not be
recognized, on and on .... Older Macs won't boot ...
Data is already hosed ....???

On the other hand, a bit off your subject, but .. I've
got a Fujitsu laptop here that has the typical CMOS
data burned to an EPROM. The only thing the battery
really does is keep the clock alive.The downside to this
is that if you password protect the BIOS settings and
forget the password, the general guidance is a trip
back to the factory .. as compared to simpy pulling
the battery and allowinf the CMOS to 'forget'
everything (some motherboards even have a jumper
set to intentionally discharge and blank those contents)

Will the customer service department of Dell help you change the battery?

My guess would be no ... if under warranty (not likely) you'd probably be asked to reurn the system to them. If not under warranty (most likely) then why would you expect them to do much of anything for you, unless you're willing to pay the costs involved.