FFOC

Log a ticket with support.

You are playing in dangerous territory. You should not be running your test site on the same environment as your production site, and they are now in some mixed up state. Every post in this thread you're introducing changes instead of taking things one step at a time.
I'd not touch anything at this point and open a support request focusing on restoring your live site into operation.
Once that's done, I'd investigate options you have on creating a separate, standalone test environment.

Thought so, specifically the theme resources.
The conf_global doesn't control those items you see in the ACP, you have to modify them to match up to your installation.
Go to the Configurations tab - create a new storage method that matches to your TEST site Back to the Storage Settings and modify each entry to use the newly created storage method. Allow it to do its stuff.  
 
 

This is why I've nominated this for the first installment of "@Jordan Invision Jigs It!" The guide is not at the level it needs to be, and you're helping highlight that. We'll get it though. Keep calm and methodical.
We'd ideally isolate these into two separate environments (two separate servers, or a minimum, two separate chrooted hosting accounts).
If you're restoring your production (live) site data into a copy to create your test site, there are some things you need to seriously consider:
Updating conf_global.php to make sure that you have a different database connection from production, making sure that you have a different hostname than production, and making sure that your values are correct. Use different mysql accounts for production and test, that do not have access to each others databases. Handling your member e-mails. Your test site will try and e-mail your members when the normal task processes run. You probably don't want this, and your members probably definitely don't want this. You need a constants.php in there. You should probably make sure you have \define('EMAIL_DEBUG_PATH','/dev/null'); as a minimum if you aren't taking other precautions (such as updating all of your member e-mail addresses in your test database to test values). Understanding that the files you are copying contain hardcoded references to your production site, so you will have to wipe cache (that's what you keep copying over) and rebuild it after you modify your domain in conf_global.php. Right now, you rebuild it by doing the "Something isn't working" option in ACP > System > Support. I hear that this will cease being quite so stupid in 4.6.  
 

We are a Ford Focus Owners Club and as such always have a banter rivalry with other makes, we set Vauxhall to appear as Whizzpopper anytime it is mentioned, for a bit of a laugh. 😎

Any unvalidated member that is older than the cut off will be removed.

There is not an option for this. Unvalidated members no longer have a group like they did in 3.x

Hi @Ford Focus Owners Club congrats on becoming the new forum owner!  
1.  Do you have IPS Cloud or your own cloud?  If IPS cloud, then send in a support ticket and they can assist.  
2.  You may want to reach out to some users on the Providers page who can help you migrate over.  They're not affiliated with IPS but many of them have years of experience with the software and server migrations.  You can check out users like @ASTRAPI @Makoto or @Spanner who can help you not only move over, but also upgrade to 4.4.  
 

Instead of going to your AdminCP, go to ModeratorCP, I have Announcements in there I can create and choose where and how they show up. 
 
On Mobile:

IP.Board 3.x does not at all support PHP 7. It is many many years old and completely unsupported.
The error in your screenshot indicates there's a database problem of some sort. You may be able to look in the /cache directory for a file with the current date to see what the actual error is (as I recall - again, 3.x is quite old and unsupported now). Your best bet realistically is to upgrade to the latest release of our software.

Good to hear it was successful! Great theming guides are here:
https://invisioncommunity.com/4guides

Well, it picked up the database, converted it etc. Said it had done it but then got a 404 error when trying to go to the ACP. Tried to go to the actual site and got this:

 
If I try to click on anything else or attempt to log in then I just get the 404:

 
I am guessing the old site webspace and PHP has something to do with this. I got excited again thinking I had a work round but alas, another wall.
 
 
EDIT: In fact disregard the above.
I'M IN!!! It worked. I had a look at the pictures and realised it was pointing to /forum which didn't exist in this. So I changed the conf_global.php info to remove that and it loaded up. Now to check around. Thank you so much for your help so far. Hopefully this is fine, I can learn the PHP side and add skins and themes as I learn to make it look more like the original.

Its going to be based on your already used license key that's already in the database. It shouldn't update anything and if you end up having an issue with it IPS support is really accommodating to upgrade issues/domains so fixing it shouldn't be an issue you'll just have to submit a ticket.

Yes.

If the php in your new server can not be downgraded temporarily to the version that supports the 3.4. forum version, you can try the method that you mentioned. i.e. install a new 4.1.10 Ipb, import the database and then run the upgrader to upgrade your database. It is worth a try imo. 
But before you try the upgrade, it is best to make a backup of your database and check it to make sure that it has been done properly. Doing that will ensure that no matter what happens, nothing will be lost.

You have to update the database as there are a ton of database changes from 3.x to 4.x. Having the server install files on the new thing and creating the config file correctly pointing to your database should allow you to upgrade the database. Sometimes you have to do it incrementally (like you may have to have a developer from the link I provided above) do it because you may need to go from 3.x to 4.0 to 4.1 to 4.2 etc to reduce on possible issues but I've upgraded databases from Jcink that are running on IPB 1.2 to IPS 4 before so its completely doable as long as the server is setup with the correct settings for IPS4.x.

These would be things outside our software and server-specific so hard to say. If you are not running Apache, you would want to look at your web server's configuration for any rewrites or redirects which may be including your old URL. This would cause a redirection back to your old server (aka current live URL).
If you are getting stuck and/or are uncomfortable in performing this, I would suggest reaching out to a qualified server administrator. There are some in our third party providers who are knowledgeable with servers and obviously, experienced with Invision Community: https://invisioncommunity.com/third-party/providers/