Given the computer is older than the retail OS X 10.6.x Snow Leopard system disc,
you should be able to buy that, use it as a bootable system (start with C key held)
and be able to check, repair, re-set password, install a fully new OS X version, or
other utility functions including reformat erase and setup a new hard drive, etc.
However the original system discs which were included with the MacBook2.1 (two
macbooks used the 2.1 identifier) were much older systems. The model in question
is the second build in the MacBook series, the first was MacBook1.1.
The original system would have been Tiger 10.4. and the original install disc set
would have included certain (vintage) applications for use under Tiger OS X 10.4.
Those old applications would not be suited for use in Snow Leopard 10.6.8.
The iLIfe and iWork suites of software, in addition to the OS X, when piecing together
the software installers for a whole system (after the original was left behind) is how
to get the later upgraded system for use with OS X 10.6.x as these are on DVD media.
And those kits, other discs than OS X 10.6 Snow Leopard, probably aren't available
from Apple Store online anymore; I see iLife '11 (iphoto, garageband, imovie, iweb)
and iWorks (pages, keynote, numbers) are not offered by Apple; if needed, those old
versions that are suited for the computer you have, under Snow Leopard 10.6.8, may
be found by looking into Amazon or ebay resellers; and should be retail disc sets that
were not included with other specific computer models which had grey label discs.
After using the Snow Leopard 10.6.3 install DVD and have a running system, update
to the full last step of OS X 10.6.8 itself -- not including later application upgrades:
Mac OS X 10.6.8 Update v.1.1 -- download update step from 10.6.x to 10.6.8
Grey-color label 'install restore media' DVD discs from another computer build model
or type of Apple computer generally cannot be used in models outside of their own.
So retail discs are usually preferred for iLife and iWork suites, and for systems not
included with the computer itself when new.
After upgrading the computer to a full OS X 10.6.8, then the App Store online is then
accessible. This assumes the OS X 10.6.8 Snow Leopard is owned by the same
person who is looking to upgrade the system to a later OS X from the App Store;
because an Apple ID will be associated with the installation from then on, once the
App Store is used to upgrade to a later disc-free OS X version. Be sure to keep the
OS X 10.6 Snow Leopard retail installer if/when it is bought, even if the computer may
be upgraded to OS X 10.7.5 Lion (a purchase, not free) since you could use the DVD
media to revert the computer to the better Snow Leopard, as it was preferred by many.
If the reason for upgrading an old MacBook2.1 is due to purchasing a later iDevice or
some other product such as an iPhone, iPod, iPad, Apple Watch, etc; be sure to read
fully the details on what OS X versions are supporting those products because an old
MacBook may be unable to run a new enough OS X to support most recent iDevices.
These are cautionary and may be considered an alert to these possibilities.
When you contact Apple about the original OS X system for the MacBook2.1
they may tell you if that vintage OS X restore install system kit is available or not
and if not, offer to sell the Snow Leopard 10.6.3 retail DVD. Get that. It won't have
those other applications, but the system it does provide is better for the computer
than Tiger since the 10.4.11 system is limited, vintage and may not be available.
When upgrading to a later newer OS X, sometimes hardware update is required
for better performance; so note the installed RAM memory total, as more is better.
A separate idea, if the hard drive should be worn or failing, is to upgrade it to a
faster spin rate 7200-RPM version, as the old MacBook shipped with slower 5400
RPM drive, and this relates to efficiencies in temp file swaps, virtual memory and
a quicker acting computer; the memory itself is an easy upgrade but limited in total.
The hard disk drive is a bit more difficult. See the iFixit mac repair guides for ideas.
In any event...
Good luck & happy computing!