A DMCA notice (which deals with copyright, not trademarks) does not require that a host close down a site; it deals with the removal of a specific infringing work. Generally speaking, the host is not required to have a DMCA information page or safe harbor page and is not required to comply if they are not interested in seeking the safe harbor provisions. Your best option will be to seek an IP attorney to send a formal demand letter to the ISP, and follow up with litigation if they continue to refuse.
My colleague is right, a DMCA takedown notice doesn't require the the closing of the site, unless the entire site infringes, which seems very unlikely, and it only covers copyrighted works, not trademarks. It's also true that no one is required to have a DMCA policy, if they're willing to forego the immunity that having one and complying with it affords.
Perhaps your letter wasn't worded correctly, and the recipient rightly concluded that you were doing your own legal work, and not doing it the right way, so you weren't likely to follow up.
I don't know what you mean by "personal" copyrights and trademark - have you actually secured those IP rights by U.S. copyright Office and USPTO registrations? If it seems silly to spend money to enforce your IP rights, then maybe you can't afford to have IP rights, because that's sometimes what's required to keep them.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
My colleagues are correct that an internet service provider and web site owner are not required to have a DMCA policy or "safe harbor" page, tho it seems reckless not to. Perhaps the ISP and/or site owner is counting on people's unwillingness to go to court to protect their rights, since that's what they have to do it the DMCA procedure is not available. Both the ISP and the site will be liable for the infringement in this situation; contact a qualified IP lawyer where you live or work or where the offending host and/or website owner work or live and discuss a suit for willful infringement. You do have your claim to copyright federally registered already, yes? That is a prerequisite to filing a federal suit for copyright infringement - in many federal court circuits not just applied for but issued. Once registered you can claim actual damages or "statutory damages" for infringement occurring after the effective date of the registration (which is the date of filing a complete application for registration) - these run from $750 per infringement to $150,000, in the court's discretion in the circumstances.
The above is general observation and not legal advice. No attorney-client relation is established by this post between me and you or any other reader. Best wishes.
I will add the following comment: DMCA takedown notices must comply with certain technical requirements to be effective. An internet service provider which complies with an improper takedown notice can face significant liability in the even that the takedown notice was improper in some way. Remember, sometimes the parties who post allegedly infringing material are offended when an ISP complies with a takedown notice. If the takedown notice is technically insufficient, than most ISP's will not comply.
My guess is that there is something wrong with the takedown notice. These are sophisticated and complex legal matters, and takdedown notices generally should be prepared by or under the direction of experienced counsel. My recommendation is that you or your client retain experienced IP counsel to assist you in resolving this matter.