Hey there, welcome to the forum!
Nobody would ever consider rejecting you, you're obviously a very sincere person, and if you're here looking to improve - that shows your trying to do whatever you can.
First of all, I can say I understand your turmoil, it's not just you who's going through this, it's every serious person in our generation which is so infested with filth. We all made a promise to G-d, and we all are currently experiencing difficulty keeping to it.
How can I pray to G-d when I continually turn my back on Him?
.... yeah, I used to beat myself up with that line obsessively. But ultimately I realized the real 'betrayal' was not 'losing my sense of logic and doing something stupid'. It was much deeper than that. All along there was an underlying cause I was simply unaware of.
I have two pieces of advice for you.
1) Mention to your Rabbi that you struggle with these things, and that your willing to do anything to cure it. He might have some good advice or know someone who does.
2) NEVER let the good be affected by the not so good. All because you have not
yet been successful in your service of G-d in one area, that's not a reason to slack off in other areas. On the contrary, at times the only way we can deal with our falls is by doing a little extra Torah, or accepting a little something on ourselves from then on.
I have a very good feeling about your whole story. You sound like a person we would be proud of to have as one of us. You just gotta ride out the tough parts in life. In the end - it all turns out for the best.
Hang in there!!