Error for customer trying to 'register' at checkout

Rather than guest checkout, register/continue button causes this error:

"From: (our https website name).....Error

Nothing else. 1.5.5

Not sure if this is server issue or something errant in our code. Nothing much changed in recent months.

Guest checkout is fine. If clicking 'log in or create' from the home page, the only issue there is the asking for Tax ID for no reason. We've never required it.

Thanks for any suggestions.

Looks like a damaged file in catalog/controller/account or /catalog/model/account or /catalog/view/theme/default/template/account

would start to reupload fresh files from same version.

next check in admin sale customer custoemr groups and see if the requiered fields are correct.

Any cleu when checking your error files.
Also when trying to access your error log, its asking for login, did you htaccess protect some folder on your site, only admin can be password protected, all other cant.

Victor, thank you for the suggestions.

We have restored the files suggested, and cleared up a few other items, but nothing has caused the change we're seeking.

Error still exists on that checkout point, though not on the log in link at the top right.

This error shows up daily in the log:
2015-11-17 2:17:42 - PHP Notice: Undefined index: parent_id in /hermes/bosnaweb02a/b2308/sl.bumperpl/public_html/catalog/controller/module/category_superfish.php on line 81

And has for years. Beyond that, nothing much else.

Any further thoughts welcomed. Thank you again.

Still no joy on this one.

Can register from home page, upper right link but cannot register on checkout. Refreshed and updated with prior files, no change. This one is really stumping us.