Note: the following is not my sites name or subject matter it just being used as an equivalent example.
Consider that ExampleArchive.tld is registered but nothing is even parked there. The contact details are shady and I've been unable to get a hold of anyone about the domain.
Should I be willing to lay down sedo commission to get a broker to acquire it for me (plus $500-$1000 for the purchase) or is the domain TheExampleArchive.tld (which I have) strong enough.
My concern is that it's already fairly long and most people will just come to know the site as Example Archive. Is the additional "The" in the domain damaging at all?
Also I risk ExampleArchive.tld eventually becoming a competitor or at least a drain on SEO for my site. Is it worth it to go after?
In my opinion it depends on two things.
Lets face it... it would be nice you have a perfect domain however content and what you are providing on your site are much more powerful then the name itself.
I say if it bothering you that much get a different domain all together for $10. Don't go though the hassle of acquiring the domain especially when you are a start up and there are other more important things that will require money and time.
In terms of your risks to being successful the choice of whether 'the' is present in your domain name is a very small factor. In your position I would not bother with trying to go for that domain name. Spend the money to reduce one of the bigger risks in starting up.
For SEO, yes, exact match domain is beneficial but it isn't everything. It is all about building the authority of your domain until it is a brand in Google's eyes. This consists of building good content and good authoritative links into your website. The fundamentals of SEO, onsite and more importantly offsite should be focused on and the other competing domain name shouldn't be a problem. It is unlikely they are going to be able to build a brand around their domain name unless they too have a similar product offering and resource.
Can you think of another domain? Like Lamar said - if you have another domain name idea you can use then that is definately worth thinking about. The principle of having a short, memorable and easy to type url should be adhered to as much as possible. Depending on what industry you are in and where your traffic will come from you may not be relying on people typing your url to reach your website if they are all coming from referrals and organic search.
What's the basic question here? For a start-up that needs to be found (which I'm guessing is most of them!), it's whether the domain name is going to be
There are fashions for which of these is best, but they're all viable.
So if I get you right, you're looking for the first of those, but someone is camped out on the perfect name.
Without question, if you register (say) themowersharpener.com, then the person who has mowersharpener.com is a problem you will face - whether just by drawing off traffic to some ad-packed site or by selling the domain to a rival. That's only a problem in the success case, and only for a limited period (if you grow enough then you can get protection against abuse such as passing off) but it is a problem. Me, I'd be prepared to live with the risk if I thought it was the (next to) perfect name.
But maybe go through the work of identifying some possible type (2) and type (3) names. In the end, a great name is a way of reducing marketing costs - it's about efficiency. But the primary concern of a start-up is effectiveness, creating and delivering valuable propositions for your customers.