What happens when you try to blog? Does the new page just not open? Does your computer crash? Do you get a small error at the bottom of the page? Does the blog popup page open and it disallows submission of the blog? Does the blog page close and the submission doesn't appear?
It could be the pop-up settings. I would think if you get the pop-ups for comments that that wouldn't be the case. Did you change any privacy/security settings on your computer?
Have you tried downloading a different web browser in the interim and trying on that? Though I have some privacy concerns with it, Chrome is a really light browser resource wise. Has your husband or daughter tried to troubleshoot this?
If you have a library near by that you go to that allows internet access, maybe sign up for some time?
Check in with the SP tech forum and see if anyone else has had these issues. Have your browser and version ready.