One of the reasons I was so motivated to change the tagline of this site recently was because the new site design contained the site's logo as a background image. The logo link was a regular static link, but it had no anchor text, only a link title to describe the link. If you do not look at the source code, the link title attribute can seem like an image alt tag when you scroll over it, but to a search engine they do not look that same. A link title is not weighted anywhere near as aggressively as an image alt tag is.
The old link title on the header link for this site was search engine optimization book. While this site ranks #6 and #8 for that query in Google, neither of the ranking pages are the homepage (the tools page and sales letter rank). That shows that Google currently places negligible, if any, weight on link titles.
I have ranked other sites for more competitive queries based exclusively on internal links (without thousands of links from other sites, like those pointing at the SEO Book home page).
Does the image alt text carry more weight? In a word, yes. Here is now I proved that to myself through yet another site error. :)
One of my hobby sites has a fairly flat file structure, and some of the internal pages are somewhat linkworthy. The site was not marketed aggressively and the only sitewide link to the homepage was the logo, which I forgot to put an image alt tag on. Google ranked 2 pages on the site well for the core keyword, but neither of those pages were the homepage. I noticed the lacking image alt tag, fixed it, and within a week my homepage was outranking the other pages.
If the only link to your homepage is a logo check the source code to verify you are using descriptive image alt text.