Can a girl who was married for 4 weeks get re married to a kohen? Even if the first marriage did not have any sexual relationship?
Any girl that was married and got divorced, may not marry a kohen. This applies even in olden times when they did kiddushin (betrothal) before the actual wedding, if she got divorced even before the actual wedding she was still not allowed to marry a kohen because she is considered a divorced woman for this.
May H-shem help you find your correct soulmate soon.
Shulchan Aruch 6-1.