There are a number of issues here. Firstly, since this happen after checkout, we are unable to see what is happening, so would need a much more specific explanation than simply that you are unable to browse - who are you? the customer, other visitors, the administrator? What stops you from browsing? Page not found, browser crashes, page freezes? How are you trying to browse? Are you logged on or not? etc.

The template is a very old fashioned one generating heaps of tables. Zen Cart hasn't done this for almost two years. What version of Zen Cart are you using? If it's in the 1.3.x series, these tables must be coming from the Algozone template. What version of Zen Cart has that been designed for?

Have Algozone changed how the checkout works? What was their response when you asked them about these problems?