Suddenly I can’t edit files – file not writable

For some reason I can no longer edit any files on any of my WP installs (using the WP editor). At the bottom of each file is this line:

If this file was writable you could edit it.

All along I have always had everything chmod 644 and had no problem. My server provider has just moved all of my accounts from one machine to another. I inquired there about the sudden change in permission and they told me

Basically you’re looking at the difference between mod_php and phpsuexec here.

You’ll need to change the chmod before you can use them again.

So what do I need to have these changed to? I tried 755 and that still didn’t work.

This also appears to be affecting some plugins, as I’m getting some error messages on a few installs that mention various plugin files in the message.

I’m very weak on understanding chmod (I do understand owner, group, public – although don’t understand exactly what a group is – I just don’t understand what to use when) so any help is greatly appreciated.