1) check the newsstands for Linux magazines, as they often have on the cover (or inside) a Live Distro or three on a disc... But they also now mostly do DVDs, as their media of choice, which probably wouldn't work for your optical drive, so you can fall back on...
2) make one yourself. You need a (re)writable CD (again, not a DVD) and also a writing-capable optical drive (depends on how old and/or how low budget your equipment was, but I'd say you have a good chance of having that already, even if you don't use it. Check for CD-R, CD-RW or one or other of +, - or even combined +/- symbol after DVD with R, RW or RAM after
that, usually moulded onto the facia of the tray, depending on antiquity and how many of the old standards the device is geared to support, because it was a bit "VHS or Betamax or Video2000", in the early days. Best you get a CD-R media, though (all should write to that, and the laptop drive
should1 be able to read it,) if you don't already have some handy.
Then you need software able to write an image to a disc, on the working machine. Roxio or somesuch might be installed, newer versions of Windows
may be able to do this natively (they can write files, but tbat's not the same thing) or some Distros have utilities they have created/recommended especially for the task. (Mostly that's USB writers that I m used to, though.) Something like
http://www.ntfs.com/iso-burning.htm might be useful (but I haven't vetted the site or application, so take care unless someone else is willing to give it credibility).
One suggested Distro is called Puppy. The page
http://puppylinux.org/main/Download%20Latest%20Release.htm gives you various downloads (go for the top .iso file download, probably, but read around the site if necessary - there's also a 'purchase a CD' thing if you
really can't handle the making of a disc yourself). And, if nothing else, you can continually perma-boot from that disc to get a simple (non-Windows) usage out of the laptop.
Or there's specific "rescue" distros, as can be seen at
http://lifehacker.com/5984707/five-best-system-rescue-discs with five examples. You don't need the AV/malware-removing features, and not all of these are Linux discs, but all (if you can understand what tools you do and, especially, what tools you
don't need to use) seem to have the ability to rule in or out the possibility of keeping your old drive or confirming that it would actuaully need replacing to go further.
Sorry, but that's a lot of information to take in, I know, and I'm sure others will want to add to/rescind some of my advice, even before you come back with rather specifc questions about what I actually
mean by something I may have skipped too lightly over...
1 There was a laser-colour change, with (re)writable media, around that time, that meant some older CD-ROM drives couldn't read some of the writable discs. But, for the price of a few discs that you can use the rest for other things anyway, at very little 'wasted' expense as long as you don't have to buy a new (writing) drive to start with. Or so I would say, YMMV.