Theme appears broken after routine updates

Hi,
On Monday I ran some routine wordpress updates and after that the theme appeared to be broken. We tried rolling the website back to previous versions using updates, but even going back 2 weeks, the site would no longer load properly. All pages were blank except twitter feed shows up.
Any idea what could be wrong? Has this happened to others?
Theme appears to be unstable.
Site loads fine with other themes.
I am using this theme on another site and now I’m afraid to update that one.
Here is web address, though currently we have reverted back to old theme so that it actually works. http://mcveymanagementsolutions.us/
Thanks for any insight.

Dear Luna,

Could you confirm if the issue still remains while all non-required plugins being disabled?

Regards,
Kharis

Hi Kharis,
Thanks for your response. I disabled all the non-vital plugins and it started working again. Then I reactivated them one-by-one. Still OK. The strange thing is that I tried this process when it first broke and it remained broken. What do you think was going on?
Also, why didn’t my backup versions work? That’s a mystery to me.
I would really appreciate your ideas about what the problem might have been. I really like this theme and want to keep using it, but I’m a bit worried that it might break again.
Thank you,
Luna