Admin pages not found, images missing and redirect loops

I’m having trouble with my website (thelanternproject.com.au), sometimes the pages don’t load properly, images are missing (and now widgets are too seeing I’ve had to turn so much off to try and work out what has happened) and sometimes it seems like the CSS doesn’t load at all and text just runs down the left side of the page.

I’ve increased the WP Memory limit via config file changes, I’ve checked my .htaccess file settings and I’ve checked the _options table has the right values for the siteurl and home.

I often try to login to wp-admin and get a Too Many Redirects error, or if I do log in, when I try to access various areas I get Page Not Found errors. Generally after a few minutes or after refreshing the page a few times or clearing my browser cookies and cache I am able to login but then the problem happens again when I return to the admin and try to do something.

I’ve manually reinstalled WordPress using the instructions provided here.

I’ve disabled the whole plugins folder numerous times and I keep clearing my cookies and local cache but still the problem persists.

I’m concerned that if I create another copy of the site using the database and files backups that I have that I’ll just recreate the error.

The most recent plugin I had added to the site was Gravity Forms (I had set up three with conditional logic and I thought initially the jQuery might have been conflicting with my theme or WP) but even after turning the plugin off I continue to have the problems.

I have no idea what to try now. The site, when I can see it, looks a disarray because I’ve left off various plugins which were generating content. If anyone has any suggestions (short of rebuilding) I’d be most grateful.