I just installed OpenOffice 3.0 from the repo into a fresh build opf Vector Linux Light to see if I could replicate the problem. It works perfectly well here. So... I have to assume either you installed something else that conflicts with OpenOffice or else you are missing something OpenOffice depends on. Since OpenOffice isn't supposed to have any dependencies (no slack-required file) the latter is unlikely but possible. A third possibility is that you somehow accidentally deleted part of the core VL Light system that OOO needs.
Let's start by looking for conflicts. Please post the output of:
so we can see what's installed on your system.
eMachines EL-1300G desktop, 1.6GHz AMD Athlon 2650e CPU, 4GB RAM, nVidia GeForce 6150 SE video
CentOS 6.5 (will try VL64-7.1 soon)
Toshiba Satellite A135-S4727, Intel Pentium T2080 / 1.73 GHz, 2GB RAM, Intel GMA 950
HP Mini 110 netbook, 1.6GHz Intel Atom CPU, 2GB RAM, Intel 950 video, VL 7.1