I have always had a very hard problem sleeping, and
I thought if I could find this I could loop it to play all
night. The longer the duration the better.

What episode was this sound you refer to, is in?

Aha, a subject I am familiar with (the insomnia and the enjoyment of the sound fx)
There are literally dozens of extended/looped Tardis sounds on youtube. Search "Tasrdis hum" or "Tardis ambient" and you'll be able to find everything from the 1st Doctor to the 12th, in any length you need (I've seen 12hour loops). No matter the version, it seems many, many people find it a calming/soothing sound to drift off to, along with similar SF sounds like the Enterprise D warp core (one of my personal faves)
This might be close to what you're after: https://youtu.be/pcZjRiAvszM

Capnzathrus, if you're referring to the "Materialisation Loop" the TARDIS got stuck in (Series 5 episode, "The Lodger"), you can find two versions of it here: https://groups.yahoo.com/neo/groups/TardisSounds/files. You'll have to join the Yahoo! Group for TardisSounds, but it's a free membership. One of our members created the Group since the Forum doesn't support sound files, and all of the files are free downloads (most in WAV and WMV formats, though there are a few other formats).

Once you're in the Files section, you'll find both versions of that sound in the "matt smith 2010 tardis" folder.

I hope this helps.

Dino.

Thanks. Made one.