My girlfriend is Jewish and was raised in a Conservative home. She had four years ago been married in the courthouse to a Jewish man. According to her they both conducted a secular marriage in which the traditions were not followed. This is one reason she wants to divorce him. The other, is that the man has denied her sexual relations for over four months. Since I want her and I to be married by a Conservative rabbi after she divorces civilly, will the Conservative rabbi insist on a get even though the original marriage was civil?

If you are concerned solely with accepted practice in Conservative Judaism, you would have to ask the Conservative Rabbi whom you choose to officiate at your marriage. 

However, if you would want the route you take to be accepted by all Jews in the future, your girlfriend would have to ask it of an Orthodox Rabbinical Court. Most likely, an Orthodox Court will rule that there was no marriage in accordance with Jewish law and therefore your girlfriend does not need a get. I must emphasize the wisdom of getting that ruling in writing from a recognized Orthodox Court, so that if any of your future offspring either move to Israel, or wish to marry in an Orthodox ceremony, they will be free to do so, unencumbered by any doubts as to their personal status in Jewish law.

I suggest your girlfriend turn to the Beth Din of America for a consultation (