For divorce you must apply to Statsforvaltningen first - as I wrote you cannot apply directly to the court. Statsforvaltningen will then contact your husband for his consent. If he will still not give it, you must actively demand that the case be referred to the court. Statsforvaltningen will do that. You do not need to be present yourself, you may hire a lawyer to represent you in court. When you have been separated 12 months you have a RIGHT to get divorced. The only thing your lawyer will have to show in court is proof that you were separated January xx 2010, and that you and your husband has been living apart since then. In your case this is no problem. Also it is no problem if you could not leave your husband on exactly the day you separated. The authorities accept that people who separate may need several weeks to arrange to move.
As for your chances for getting a visa, it depends on whether you overstayed your former permit. If it says in the letter you got from Udlændingestyrelsen that you have been banned from entering Denmark for a certain period, then you will not get visa.
If it just says that your residence permit has been annulled, and that you have to leave on a certain date - and you did that - then you would have a reasonable chance of getting visa. Your boyfriend will need to send you an invitation (there is a form on
www.nyidanmark.dk), and state that he will 'house and feed you' during your stay. The authorities MAY demand that your boyfriend further guarantees for you by depositing about 60.000 kr. in the bank. The 124.000 kr. is the amount needed when someone is applying for reunion with a spouse.
You will need to take out a travel insurance, and you should document that you have a reasonable amount of money in your account, as well as a reasonable amount of cash in your purse when you travel. You should check the information here:
http://www.ambbangkok.um.dk/en/menu/Con ... irlfriend/
Please note that you as a tourist do not need to pass any language or other test. That will only be necessary if you get married to your boyfriend and apply for residence permit.