you need a floor scraper,cost about $6.00 from home depot.(make sure the blade is in the correct way, its often sold with the blade in backwards)while you are there pick up a gal of kilz (kills) primer sealer and paint that on the cement after you finish with the scraping....good luck

You can easily do your job removingthe foam and adhesive using PEEL AWAY 5 paint remover. Visit the web site at www.peelaway.com

Thank you, Carpetman and Hy. I decided to try to "dry scrape" first and use Peel Away if that didn't work. Used a lot of elbow grease but was successful with the scraper bought at Home Depot. I cleaned with Oda-Ban bought at Sam's Club, but still smelled a faint urine odor. I purchased a product similar to Kilz made by Zansser called BIN and applied it to the floor. This seems to have done the trick. I am quite relieved, so thanks for your help. One last question: I will probably encounter similar issues to a lesser extent upstairs with a plywood subfloor under the carpet. I would like to replace with hardwood floor - should I try to clean and seal the plywood subfloor or have new plywood put in?

the sealer you used will do fine on the plywood...good luck

Just discovered the upstairs subfloor is particle board, not plywood. Still OK to use BIN to seal? Also, was planning to install hardwood, but have been told I can't over particle board subfloor. Considering laminate now, is there any comprehensive comparison around about the vast array of brands, installation choices, price comparisons, etc?

the sealer will work on the p-board....why not use a hardwood floating floor,take a good look at "coastal woodlands" by bruce at your local home depot....this is a very easy d.i.y. project,also when you concider the nail on 3/4" solid wood floor sit's on top of the tounge,the floor is about as thick.
if you choose laminate, all of the major brands are about equal if you are in the $3.00/4.00 price range,home depot carrys one called hamilton (by shaw)at $2.49 or $1.99 if its on sale.....good luck