As to whether Google penalizes (special attention to this word) a site for being stagnant.
The answer is "No." Absolutely not.
Here is what you are missing. Google uses a TTL style metric to gauge any pages freshness. TTL stands for Time To Live and is used to do two things: one, gauge how often to re-fetch the page; and two, use as a metric for the SERPs.
Google does recognize that not all pages will be fresh or should be for that matter. There are a bunch of historic reference pages out there that Google recognizes as highly valuable even without a bunch of back links or activity. So any page that has gone stale still has value in Google's eyes. However, if all of your pages go stale and no new ones are being added, it is likely that Google will visit the site less, visit the sites individual pages less, and not adjust SERP placement until there is a large shift in the metrics. Google may also assume that the site has been abandoned. Just going back to your pages and updating them, fix errors, add a few, re-vamp the look and feel a bit, and so on, will really go a long way.
Think of it this way. If a site is stagnant for a year, why would it take just a month or two to get it back up high in the SERPs when so many other sites have been active? It takes a long time, but any site that has been dormant can perform just as well as any other just by updating it again. Think of the TTL as a rolling average. You will want to look up rolling averages. They are hard to move but will. It will take a long time to get a longer TTL time to a TTL time that matches your competitors.
There are several things that have to happen. You need to build domain trust. This is part of that Trust Flow and Citation Flow metric you quoted. The numbers you cited are low, but better than 0. Time, activity, inbound and outbound links, citations, and so on will change this along with other metrics. This is your foundation. Freshen up your content and add new content to reduce TTL times. Reference other high quality sites with outbound links. Change you inbound link ratio bad:good so that good outweighs bad by a healthy margin. If you can, use social media. I like Twitter (though I do not use social media at all). Twitter returns targeted users better than most. Facebook is the other one, though for me it is too much work. It is like having another site. It will take time to build your site back again. It will be a bit harder but far better than starting a new site. You will want to build a site reputation and branding and that will just plain take time.
I will quote one of my favorite T.V. shows from the 70's Kung Fu,
BTW- I like your site! It is pleasant to look at and simple. Simple is always best!
I assume I am looking at your website. Here is some of what I see.
title tag is too long. Make it about 45-50 characters. The
title tag is used for the SERP link. The actual measurement is 512 pixels (like that is a helpful metric). This is means that wider characters such as W, M, G, D, and so will eat into your space. You can use Fetch as Google in Google Webmaster Tools to play with SERP listings. Your
title tag should have your most important keywords.
description meta-tag is too long. Make it 160-170 characters max. It should also be conversational. The
description meta-tag is used for the SERP snippet and should be about 2-3 lines. As well, your
description meta-tag should have your most important keywords plus the ones likely best used to find your site/page. The
description meta-tag keywords do not carry much weight, however, are often matched when doing a search query so they are very important.
I am now thinking that it is best that keyword tags should just plain disappear. I used to argue that it should be used just in case there is a benefit, but now I am seeing a benefit for not having it. I just whacked most of mine and I can report back later on the effect.
There are a bunch of reasons why a
title tag and
description meta-tag are not used in the SERPs. If you do them right, they will almost always be used.
You do not have an
h1 tag. This is important. It should be closely related to the
title tag without being a copy or close copy of the
title tag. You can use the Cheap Health Revolution for this which you already have.
Under each image, you have a paragraph tag that is likely better served as a header tag. You can make it an
h2 tag and make your current
h2 tag an
h3 tag without fouling up the look and feel. You can just adjust your CSS file for this. Or you can just make it an
h3 tag and modify your CSS. Experiment around. These keywords, however you chose to do it, should compliment each other from
h3 from a search perspective.
Your home page was a bit slow the first time. As well, you have a lot of requests that make the accumulative load time about 6.something seconds the second time around though the page and resources do each load quickly. Consider if you can make fewer requests or if you can push the slower ones to the end. Some people swear by sprites for images. Something to experiment with.
Consider placing the ad below your header or at the bottom of your header. You may want to experiment with this. However, it is said this is the best place and not at the very top. This will push up your important content code and presence in the users mind. Something to think about.
Consider putting your social buttons at the bottom of your header somewhere in the content area just above the content. Some people swear by floating social buttons, but I have to admit I am not sure about this as being the best advice. I see the most successful sites have their social buttons at the top of any article. Placing the social buttons somewhere in the line of sight may encourage more activity.
I am sure there is other advice I can make, but for now, that will be a good start.