Remove the carpet - it is never going to be a good solution. The concrete might be fine and then adhesive removers and paint might work great. If not, there are vinyl wood planks (pick the whitewashed finish look) you could put down to make a "deck" since it is under cover. Just put a real wood reducer at the top of the concrete walk.

thank for your info. Travertine sounds beautiful but over my budget - I'm 81 and income is limited. How thick are the vinyl wood planks and how to attach them? It sounds nice - the off-white look, rain and snow blow in but not much as this high plains area is very dry. What kind of store would carry them? We have some big box stores here but we are hundreds of miles from a big city.

At 81 I am pretty sure the last thing you want is a surface that might be slippery.While I normally do not like outdoor carpeting, I do think it might be a safer and less expensive option for you. If the old carpeting is glued down and the concrete has to be cleaned to get the old glue off in order to have bare concrete the labor cost could be too much. I would talk to several places that sell indoor/outdoor carpet and get their quotes for the carpet and price for removal (and disposal) of the old carpet and installation of the new. A medium grey should be dark enough to hide traffic dirt, but not so prone to fade as a black might be. By the way I think your home looks quite charming.

Here is a link that is just to one product. Both Lowe's and Home Depot have these peel and stick options. http://www.homedepot.com/p/t/202819076?productId=202819076&storeId=10051&langId=-1&catalogId=10053&MERCH=REC%2d%5f%2dproduct%2d4%2d%5f%2d202885480%2d%5f%2d202819076%2d%5f%2dN#specifications

Stamps has mentioned some important ideas - avoiding anything that could be slippery and being sure to ask for disposal of the old carpet! I'd sure hate to get stuck with that! I will take a look at the peel and stick options.
We have a Home Depot here. Thanks for the comment on the house - I get many compliments. I was afraid
the porch roof would make the house dark but it does not at all - the french doors let in so much light. I am sooo ready to have flowers blooming again. Thanks for your comments. Nancy