If the problem persists, uninstall K-Lite & reinstall (simplest solution).
As Dias pointed out, some people do have problems with the K-Lite package, mainly because people don't know which codecs they need to install individually & so go for the full install, installing loads of codecs they'll never need. Why that would cause a problem I don't know, perhaps it's a conflict issue.
Personally, I would uninstall K-Lite then install
FFDshow on it's own (FFDshow is bundled with K-Lite & does most of the work anyway).
If you want to spend a bit of time researching & installing additional codecs, you can learn more about them & download individual codecs from
here (well worth a bookmark!) there's also a forum & just about every free video tool worth having available to dl aswell.
If for some reason a video doesn't play (FFDshow supports AVI, DivX, XviD, WMV, MPG, MPEG2 (SVCD, DVD), H264, AC3, DTS, AAC) then you can use a codec analzyer like
CodecInstaller to look at what codec the file needs.
Hope this helps...