Just in case look at your analytics first. You might find a few gems like a very heavily linked forum thread that was picked up by online news sites or a very well written, super long post that are worthy of preserving. I doubt you will find them but you never know. If you do find them consider converting these rare exceptions into static pages on your main site which you can then 301 redirect.
If you think the site has a content penalty, then I would err on the side of deleting more and preserving less.
I'd noindex the forum and keep it. Maybe it will add some value to your visitors in the future.
I had a similar problem a few weeks ago and am certain, that my site was hit by Panda because of low quality forum posts. Instead of deleting everything, I wrote a script to check the average post length of the thread and the total word count and set all threads to noindex if they don't meet the minimum post-length and total-word-count requirements. At the same time I set the posts per page to 20 (instead of 10), so the wordcount per page goes up (which seems to be one factor of Panda). Bottom line: I noindexed nearly 4000 threads and only kept 650 high quality and lengthy ones.
Of course, if the forum is completely inactive and doesn't add ANY value, you might as well delete it ;)