De-soldering chips is like any other job. It is only easy if you have the
right tools for it.
What would you call the right tools? I have desoldered bios
chips in a pinch where I only used very basic tools.
Soldering Iron w/fine conical tip
Solder
Dental Pick or X-Acto Knife with smallest default blade
Desoldering Braid (remove excess solder after chip is
removed, prior to soldering in new chip).
Flux (because desoldering braid didn't have enough in it,
and to allow high flux:solder ratio so less solder is
applied).
Basically with the minimum set of tools you heat the pins
one at a time and using the pick or knife slid between the
chip body and lead, it will bend the lead outwards and up
away from the pad as soon as the solder melts (applying
slight pressure while heating).
The catch is that bending the pins like this and heating up
next to the body of the chip may result in the original chip
being damaged. Since this method is used when the chip is
not to be salvaged, after bending the pins up it is easier
to break them off by bending very sharply against the body
of the chip, because leaving none of an adjacent lead
sticking out of the chip body allows easier access to bend
up the successive adjacent leads.
A hot air station is the better way to do it but many
people, including those who frequently work with
through-hold parts instead of surface mount, simply don't
have one and I wouldn't expect they want to buy one for a
single repair.
In some cases it might be desirable to replace the EEPROM
with a socket instead of soldering in the replacement chip.
*Some* EEPROM sockets can be soldered down with the same
(fine conical tipped) iron but they have a small plastic
piece in the center with very thin supporting plastic arms,
so that center piece can be easily snapped off so it can be
soldered from the top with the iron. It is a little easier
to use solder paste, then just heat each pin slightly, later
checking for continuity between pins to be sure there are no
shorts. I wouldn't advise this method on valuable equipment
but to save time or expense on something of less value it is
worth a try instead of paying someone more than the board is
worth to do the repair.
Something a couple of other posters overlook is that
sometimes a replacement board cannot be had, the same thing
does not exist (proprietary so a std. board isn't a direct
replacement, and OEM doesn't have any nor can it be found on
eBay/other surplus 'sites) and without same OEM board the
software licenses are void (meaning more expense and time
spent) or possibly an in-place migration to a different
motherboard won't work and again more time spend trying to
repair an OS installation or even worse to have to reinstall
everything from scratch. IOW the easy answer of "just
replace the board" to avoid spending a few minutes
soldering, does not account for all the further time and
expense to find, order, receive, then reconfigure or
reinstall the OS.
That time is a bare minimum of several hours, in the end
it's really more a matter of whether you have steady hands
and soldering skills (not just holding an iron but
experience using flux, picks, 'sinks, etc as needed for a
particular job instead of taking the beginner's approach
which always seems to be "apply more heat and solder".