Will this 3.8/4.0 swap work? How should I?

[kNeo]

Just a note here -- but you should figure out what's wrong first, because "SQL errors" could mean the database is broken, in which case upgrading will accomplish nothing.

You should also be aware that EVERY mod will break/be unusable when you upgrade, this includes vbacmps (though they do have a 4.x version). Additionally 4.x also requires you to re-customize the style/design (look of your forums) -- you can't bring over your 3.x design (if you've customized it). It took me a good month and a half to finish my vB4.x style, though my forum was heavily customized as far as styles go.

You can do some simple troubleshooting such as disabling all addons/plugins/etc... and going through 1 by 1 to see if any are causing issues.

You can edit the config file, I think this is the code:

define('DISABLE_HOOKS', true);

add that at the top of the config php file, just below <?php

This should disable all plugins that might be causing trouble; if the forums work after you do this that means a plugin/addon or something is causing the trouble. If not it could be indicative of a more serious issue.

Also contact your host, ask them if they've upgraded your php, vB is currently not fully compatible with php 5.4, for vB4 it's easy to work around, but I think it's worse for vB3s.

I am not at all that good with vB3, the last time I touched one was 6~ years ago, so you might be better luck on the vB3 section and/or contacting vB support (if you have an active license) to see if they can figure out what's up with your board.

EDIT: For the record if your database is fine, you can certainly upgrade to vB4, you will keep all users, content, etc... you will just lose mods and the style (the look) of your site.