To do the payment gateway you will need the help of someone that knows php and how to write script and follow the Chase Paymentech documentation.
I'll tell you right now you are probably better off convincing them to use paypal if it is pro-bono and has to be done by this weekend.
GoDaddy also adds to the problem. You will need to post a support ticket to get some GoDaddy-specific code since it requires a proxy server configuration for curl requests unlike any other host we have encountered.
Rename all of your pages to .php, you don't have to "redevelop" anything.
You don't need any databases. What databases do you want. My suggestion is to do it without a database if you don't have experience with databases and want to have it up by this weekend. How many products do they have? With just a donate button and trying to get it done by this weekend, you are probably better off just adding a donate button from the paypal developers toolkit and save eCart and database work for a paid project where you have more time.