"The logo does not show any tm on it or copyright statement. "
It doesn't have to.
If I use a distinctive logo in connection with my goods and services such that consumers recognize my symbol as a distinctive indicator of the source or origin of those goods or services... AND if I do so in a jurisdiction that recognizes common law rights (e.g. I believe every state of the US), then I accrue rights in that logo.
Now, the extent of what I may be able to recover in a lawsuit may depend on certain niceties about marking and so forth, but the rights are there.
One question you might explore here is whether this outfit has been using the logo in the years since they had stopped using the domain name. Just as trademark rights are accrued through use, they are also lost by non-use - more than about three years is a rough cut on whether they may have abandoned the mark.
That's the trademark issue.
The copyright issue is entirely separate...
Copyrights now arise whenever an original work of creative expression is fixed in a tangible form. They last a good long time, and get extended whenever the term of certain Disney works approach expiration. Unlike trademarks, continued use is not needed in order to preserve the copyright.
Again, notice of copyright is not required, but notice and registration can affect the types of damages that may be recovered when the copyright is enforced.
A good rule of thumb for things like this is "Don't use things that other people made." While you may have all sorts of defenses, etc., I try to persuade people to pick their battles wisely. But whenever you do accede to a demand that you question whether is justified, one should of course expressly note that you are doing so voluntarily because you are a swell friendly person, and not because you agree with any of their legal assertions.
I'm not sure what you mean by "logo included with the sale". If rights to the logo passed in the successive sales of the domain name, then the original party is probably the wrong one to be making the claim.
These comments are not intended as specific legal advice for your situation. I believe it is important for folks in this forum, who generally seem fixated on "is it in the USPTO database" or other formalities, to know that things like marking and notice are not the be-all and end-all of whether a claimant may have enforcible rights.
