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Can the rel-canonical be used to tell the search engines which page is "preferred" when there are similar pages? For instance, I have an internal page that  Google is showing on the first page of the SERPs that I would prefer the home page be ranked for.

Both the home and internal page have been optimized for the same keyword. What is interesting is that the internal page has very few backlinks compared to the home page but Google seems to favor it since the keyword is in the URL.

I am afraid a 301 will drop us from the first page of the SERPs.

I agree. The URL parameter option seems to be the best solution since this is not a unique page. It is the main page with javascript that calls for additional content to be displayed in the form of a lightbox overlay  if the condition is right. Since it is not an actual page, I cannot add the rel-canonical statement to the header.  It is not clear however, whether the link juice will be passed with this parameter setting in Webmaster Tools.

My fault for not being clear.

I understand that the rel=canonical cannot be added to the robot.txt file. We are already using the canonical statement.

I do not want to add the page with the url parameter to the robot.txt file as that would prevent the link juice from being passed.

Perhaps this example will help clarify:

URL = website.com

ULR parameter = website.com/?v3

website.com/?v3 has a lot of backlinks. How can I pass the link juice to website.com and Not have website.com/?v3 appear in the SERP"s?

The parameter to this URL specifies unique content for 25% of my traffic to the home page. If I use a 301 redirect than those people will not see the unique content that is relevant to them. But since this parameter is only relevant to 25% of my traffic, I would like the main URL displayed in the SERPs rather then the unique one.

Google's Webmaster Tools let you choose how you would Google to handle URL parameters. When using this tool you must specify the parameters effect on content. You can then specify what you would like googlebot to crawl.  If I say NO crawl,  I understand that the page with this parameter will not be crawled but will the link juice be passed to the page without the parameter?

I am already using a link rel=canonical statement. I don't want to add this url parameter to the robots.txt file either as that would prevent the juice from being passed.

What is the best way to keep this parameter and pass the juice to the main page but not have the URL parameter displayed in the SERPs?

The page in question receives a  lot of quality traffic but is only relevant to a small percent of my users. I want to keep the link juice received from this page but I do not want it to appear in the SERPs.