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@hyperionmarketing thanks for the question and for all of the information that you provided related to it. It looks like you have a few questions that I will try to answer for you. I obviously haven't seen the press release and do not know the quality, if it's newsworthy, etc.. so I'll just answer the question in general and not related to this specific Press Release for your company.

1. Non of the links or mentions show up on our discovered links and it's been over a month:

Yes, many of the websites that pick up your press release are high-quality and may have a high DA. That said, a number of reasons could make it so tools do not pick up the links or haven't yet. The first, one month is usually not long enough. A few should show up if they are indexed and discovered by month 2 (maybe sooner), maybe month 3. Tools and search engines are not instant and they optimize crawls and indexing to be efficient i.e. high DA sites get crawled often and deeper, low DA sites get crawled less often and they may not use as many resources to index a lot of the site (two very, very simple and basic examples)

2. Why has our DA not increased:

Unfortunately, submitting news releases is not a good way to build quality links. In fact, it's not a good way to build links. News releases should be newsworthy and used sparingly for most businesses.

Your news release didn't get picked up, written about and sourced, which is the main goal of news releases. Syndication could mean your news release goes to a bunch of websites that publish every press release anyone pays (<- important to remember when link building, can I pay to get this done easily? if so, meh) to distribute.

These sites get crawled less frequently are already pre-themed by Google to be syndication sites and the links do not need nofollow tags because they basically get one from Google's algorithm similar to how footer, sidebar, sitewide and blog comment links get devalued etc..

*In a few months, maybe 6, check to see how many sites still have your news release indexed. It will quickly show you the value of the links without knowing about DA, PA and all that other stuff. An unindexed link is unknown.

3. All links are no-follow, so I should get roughly 100 links, right?:

No, similar to above, Google treats these sites (or sections of websites) differently and on top of that, many of these sites publish so many news releases that your news release is pushed really deep (in terms of the site structure) and Google no longer finds it.

Tools may find the links, keep them for a bit, but they'll likely fall of in the long-run. Find the best source of your press release - possibly the PRNewswire's website, and make sure that it stays indexed on that site.

As a side note, submitting press releases to build links is not effective and is a complete waste of time if you do not do it correctly. News releases need to drum up new stories, reprinted stories will do you and the company you work for no good.

In fact, if I read the first sentence correctly - recently started distributing press releases... it sounds like you will be doing this often, which I would not recommend unless they are done correctly. It seems like you are using them to build links and that will likely do you harm - there are a lot of negative things that come along with building links via press releases. Do a Google search and you will find a lot of good information that should help you out.