First I guess you are not aware you can download a fully functional trial version of VSD from the CC store
I would suggest you do this first, you can import all the website into your copy of the program from them, or of the server, so you are on the same playing field
In the top left corner of the page you will see edit, and from there add files
Put everything necessary in there, so every time an edit is uploaded it has it on board
There is an html tool also to put your custom code required (way beyond me) but as a professional coder i am sure it will be self explanatory
Then send everything back to your client in a zipped up folder
I would suggest naming it something like feb 2013 professional edit

so they know in future which version to use
You might have fun getting them to re open and install it, simple for a techy (not me)
But when they upload it to the server all should be well in the world once more
That no doubt will be about 5 or 6 chargeable hours, but unlike their comparison, here we have laid good foundations for any future re build
Personally though sorry to disagree with everyone else on this, should you not have checked what program it was written in before offering to carry out any work on it, a quick look at the source code would or should have set off alarm bells, especially if you have never used Coffeecup Visual Site designer Build 7 for windows
Someone sends me a load of mixed broken jewellery and asks me to make a signet ring out of it, its no good me moaning afterwards that my casting is all full of porosity and splitting badly, just to discover lots of what they gave me was rolled gold or gold plated steel or aluminium, I have to test it myself first