I opened "Site A" around 4 weeks ago. I opened "Site B" around 2 weeks ago. Site A is yet to be indexed. Site B was indexed yesterday. Site A has much more backlinks than Site B. What can I say? This is on Google by the way.
One possibility might be that Site A's domain was previously banned. (been there, done that - About a week after I sent a reinclusion request just saying that I registered the domain a few months back, developed it and noticed that my other new sites were indexed and this one wasn't, that I guessed it had been previously banned, hence the request for reinclusion, it was indexed.)
that isn't the sandbox. the sandbox has nothing to do with being indexed or not, it has to do with ranking. are they quality links? are the pages linking to you in google? are they plain html, not javascript? if yes to all of those, my only advice would be wait. I normally don't even bother with sitemaps but this may be one case in which you might want to. check if you've been crawled. if you've been crawled but you've given it time (a few days) and you don't show with the site: operator, chances are there's something else going on that's preventing you from being indexed. banned domain, duplicate content, triggering a filter, etc.
1. Do the sites share the same IP? Sometimes IPs, like domains, get banned. If both sites share the same IP and you have site B indexed then your IP is not banned, which is good. 2. There are no blackhat SEO practices on Site A, right?
So, really, see the logs if Googlebot has visited your site. Probably it has but you have not noticed it. The easiest way to view the logs is using a software like awstats or similar - it depends on what your hosting provider is running but I believe that you must have a web stats program in your hosting package.