Hey guys:
Thanks a lot for your posts.
I have learned a lot, and recognize you have been very helpful, with very smart advise.
Jeffrey512 has been specially involved with us all. His ideas were the ones that got Mail.app working with my MobileMe account.
I had no luck with my POP accounts, and have concluded that the problem is not Lion, but the new version of Mail.app that comes with it.
I have tried everything for 2 weeks (10 days on this discussion) and, I decided to give up.
I followed DG4444's advise, and downoladed Thunderbird. I should have done that from day one. No problem receiving, nor sending.
So I will use Thunderbird for my POP accounts, Mail.app for my MobileMe account, and wait and see what the future holds for us.
By the way, MobileMe was down last night, so that may explain EricN's comments.
Again, thanks a lot.