Yes, there is a way but's a dirty job.
I am not suggesting it, you will bypass an issue to maybe encounter many others.
Let's use a bit of logic, it seems clear to me, even more, that the Captcha system has been re-engineered with the 3.0.6 version of phpBB (if my memories still serve).
Logically speaking I'd go with this flow-chart this time.
(That's what I always suggested to do with ancient phpBBs)
1 - update 3.0.4 to 3.0.7-pl1
https://download.phpbb.com/pub/release/ ... 3.0.7-PL1/
2 - update 3.0.7-pl1 to 3.0.14
https://download.phpbb.com/pub/release/ ... to_3.0.14/
3 - at this point is better to upgrade to 3.1.10
4 - finally you should be able to upgrade again to 3.2.0 without more issues.
Side note. Starting from the original backup (files and DB) of 3.0.4 until you get to 3.0.14 use the packages.
To upgrade from 3.0.14 to 3.1.10 to 3.2.0 use the suggested methods.
I am trying to help you to get a clean upgrade.
What does this query returns?
SELECT * FROM phpbb_config WHERE config_name LIKE '%captcha%'