The second user of a trademark ALWAYS believes that its use of the mark won't infringe the first user's rights because their two products are unrelated. There is a lot of law, therefore, that addresses whether, and how to decide whether, two products are "related." You cannot make that determination yourself. Because "[r]elated goods are those goods which, though not identical, are related in the minds of consumers" the related goods inquiry is quite subjective and only through long experience [and reading lots of court decisions] can someone come to a conclusion one way or another.
Moreover, there may be [and likely is] many more UNregistered trademarks that are already in use similar to the mark that you want to use. You must take those marks into account as well when deciding how to brand whatever it is that you're selling. ONLY your own trademark attorney can adequately provide you with an opinion on whether you are free to lawfully use the mark that you want to use. That is called a "clearance opinion" and is necessary when you know that your selected mark is already in use. You need to hire a trademark attorney licensed to practice in your state. Good luck.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
If your analysis of no chance of confusion is correct, you have a chance of registering your slogan, otherwise probably not. Still, there is a doctrine called "Trademark Dilution". If the other mark is famous and distinctive, you are at risk. For example, you plan on using "SONY" for bubblegum and you are sure no one could be confused into thinking SONY Corporation was producing it. You would be toast under the doctrine of trademark dilution 15 USC 1125(c) http://www.law.cornell.edu/uscode/text/15/1125
You know you need a trademark attorney's help. That is why you are here asking. Pick one from among those that answer and get this handled by someone who has a handle on the law in this area. Do not delude yourself into thinking this is simple. That can get you sued.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
If you file an application to register a trademark with the USPTO, and the trademark examiner agrees with you that there is no likelihood of confusion, the other company could still seek to oppose or cancel any resulting registration. Also, obtaining a trademark registration of your own does not immunize you from a claim of trademark infringement from the other company. You need to consult with a trademark attorney to advise you and help guide you in this matter.
This answer is for informational purposes only. It is not intended as specific legal advice regarding your question. The answer could be different if all of the facts were known. This answer does not establish an attorney-client relationship.