I didn't mention this earlier, but, in some cases, DNA testing can help you break past barriers as well. If you get a test done at FamilyTreeDNA, you can compare your results against their entire database. YSearch also lets you compare against everything they have. You'll need a decent number of results, probably 25-37 at a minimum, and then be willing to upgrade as necessary. After you find matches, you'll have new directions to do research, but you'll have to connect the papertrails before it can really be accepted.
I still recommend that you do some basic genealogy first to get back a few more generations before doing the DNA test, though.
If you haven't already done so, I recommend posting what you know of your family tree on our pedigree forum. All pedigrees posted on that page will be transfered to the surname project website, so that other researchers may find you and contact you:http://www.wfnforum.net/index.php?topic=2867.0
If you want to see the pedigrees and results of other researchers, please go to the project website. You may find other researchers already working on the same family lines that you are:http://www.worldfamilies.net/surnames/h/harrison
Also, here is a direct link if you want to go ahead and order a DNA test. Keep in mind that even folks that are not direct paternal/maternal decendants of this line can still get tested. To do so, find a relative who IS a direct decendant and sponsor their test for them. We provide comparison for test results for our project members on our surname websites, and you can use FamilyTreeDNA or Y-search to do a global comparison match (over 1/2 million DNA tests for genealogy have been conducted so far):http://www.familytreedna.com/DNAList.asp?Group=Harrison
Also, please check out our website if you want to learn more about DNA testing and genealogy at:www.worldfamilies.net