Oh the memories, I did the exact same thing a few times on my previous hosting providers. It's so easy to mess it up.
Take your time, make sure everything is restored.
I think I have found out why the problem is happening. It's going to be something with the fact that not only wordpress products are selected to look for, but also posts. When ajax search pro tries to pass the results to the theme, there are posts as well mixed with the product results, and I guess that post objects does not have that method, which the theme refers to, so it stops with an error.
One quick solution is to turn off the Search in posts option on the General Options -> Sources panel. If you have everything back and running, can you please try that? If I'm correct and if that works, then I might not be able to give you a quick fix to make it work with both posts and products. I've noted this as a possible bug, and if it's confirmed by you, I will fix it for the upcoming version properly.Best,
If you like my products, don't forget to rate them on codecanyon :)