Question: I've received a job offer from a former client with very nice terms, a decent pay check, just all around a great job with people I know and get along with.  

Coupled with the fact that I may not be very suited to my current job (consultancy) as opposed to what they're offering (full time business as usual).

But I've come across a hindrance.  

Upon reviewing my paperwork, I noticed that I do not have a specific document I signed.  

When I was working for this customer, I had to sign a do-not-compete clause with a different company. To put matters into perspective I'll explain the situation a bit.

* I am employed at **nice small consultancy firm**
* **Customer** was looking for a consultant that matched my skill-set
* **Bodyshop** is a provider of consultants for **Customer**
* **Nice small consultancy firm** outsourced me through **bodyshop** to **Customer**
* I signed a do not compete clause between **nice small consultancy firm** and **bodyshop**
* **Customer** stopped all contracts with **bodyshop** because of some bad experiences
* **Customer** opened up some job postings for employees to replace the consultants that were let go

Now I never received a copy of this do not compete clause, I signed it, and I think both company's have a copy, but I don't.

How would I go about obtaining a copy?  

Am I just utterly screwed if I sign something now?

Answer: 
I would simply contact whichever company was supposed to provide a copy, and request it again. If they ask why, you don't have to lie: "I wish to retain a copy for my records". It's by no means an unreasonable request or unusual answer.
Depending on the country and the company policy, you may have access to all documents in your HR file. Rather than specifically asking for this non-compete you may be better off asking for a copy of all of your documents. If HR asks why a "I'm not sure if my copy of my records is complete" is unlikely to raise any flags. The upside of taking this route is that you get copies of everything just in case there is something else missing.