can't update to next version.

There are two version 10s, 9s and 8s,
https://secure.wikimedia.org/wikipedia/en/wiki/Ubuntu_%28operating_system%29#Releases

The x.04 versions are the "long term" releases and the x.10 versions are the normal releases. Supported update paths are listed here:
https://help.ubuntu.com/community/UpgradeNotes

Which versions were you trying to update from? Can you provide the output from a terminal (Ctrl+Alt+T or from applications menu) of the following commands?

cat /etc/lsb-release

-----

As a direct workaround for that error you could uninstall openoffice and remove all its dependant software (try removing openoffice's common base package, openoffice-base-core.

not openoffice-base-core, just openoffice-core. (my bad)

I suggest you uninstall openoffice then upgrade. Should be fine

My system is 8.04(hardy). Am trying to update to 10.04, or 10.10.
As I said, I'm a caveman when it comes to doing this stuff.
I don't know what you mean by; " Can you provide the output from a terminal (Ctrl+Alt+T or from applications menu) of the following commands?".
How would I;
"uninstall openoffice and remove all its dependant software (try removing openoffice's common base package, openoffice-base-core."?
Thanks in advance!

In terminal run:

sudo apt-get --purge remove openoffice*

Then try the upgrade.