My old svn repo is no longer accessible, the physical server no longer exists. So, I'm going to be making a new one. I still have all the actual data plus newly modified and added files since. I'm wondering if it's possible to just commit all the files to the new repo. Or will I have to remove all the .svn files, and begin anew?
When you checkout a subversion repository you don't fetch all the metadata. because Subversion is not distributed as Git for example. So I am afraid you lost your history, revision changes, etc.
So as you guessed you will need to remove the .svn metada and just create a new repo and commit everything again.
It would be much easier to help you if you describe what do you mean by "svn repo died". What happened exactly? Don't you have a backup? I've never encountered a case when repository is completely inaccessible (unless it is FUBAR).
BTW if the issue is just about connectivity to Subversion server: if you still have access to the machine where your repository is stored you can always move the repository to another server.
Paraphrase of @bahrep and @golja
If you have only Working Copy and can't get accessin any form* to repository data (high- or low-level) - you lost all your history.
Can't recall Subversion's behavior in this case, but you can at least to try (for "creating new repo" as last resort)