Problems Commenting

I don’t know if anyone can help me, but I don’t seem to be able to comment on a lot of people’s blogs when I’m using my laptop.

The blogs in question have a comments box like this

As you will notice, they are blogspot blogs and I am signed in on my blogspot account. If I use the broadband PC at the house, I am able to comment, but not when I’m using my laptop.

Some people have managed to adapt their comments pages so that it comes up with the same comments box that shows on my posts, but I’m not sure what it is that they’ve done.

Can anyone explain what’s going on? Is it something I can configure on my laptop or what do the bloggers need to do to change things at their end?