You've got almost no chance of getting this trademark registered in the same class as someone else's registered mark. Registrations are done per class, and the USPTO would consider these businesses, both in service mark class 38, similar enough that consumers would be likely to be confused by two companies using the same mark.
This is from the USPTO's Basic Facts, linked below:
"To find a conflict, the marks do not have to be identical, and the goods and/or services do not have to be the same. It may be enough that the marks are similar and the goods and/or services related.
If a conflict exists between your mark and a registered mark, the examining attorney will refuse registration
on the ground of likelihood of confusion."
The USPTO won't tell you to stop using the mark, they only regulate registrations, and they don't determine disputes. If you've been using this mark for a long time and have never gotten a cease and desist letter from the other company, maybe you can continue to co-exist with them, as maybe they think your services are different enough and they haven't had their customers demonstrate confusion so that they're even aware of your company.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
I partially disagree with Ms Koslyn - there really is no way to tell what the USPTO might or might not do based on the info provided. If the mark is important to you, hire a trademark attorney to complete a comprehensive search and to give you further guidance.
Notice: The below is for educational and informational purposes only, is not a reflection on or a representation of any views or opinions held by my employer, and should not be construed as legal advice. Nothing herein is meant to create an attorney-client relationship.
You state that you have been using your mark for 15 years, and that the other party's registered mark is incontestable. This means that the other party's mark has been registered for at least 5 years. You should review the USPTO records for that registration to find out the first date of use that was alleged by that registrant. Since trademark rights in the U.S. stem from use in commerce, if this other party has earlier rights in the mark, you should tread carefully, especially if you believe that the service areas might be similar.
You state that you "maintain computer systems", but would like to file a trademark application in Class 38 for "service provider". It is not clear exactly what types of services you provide, but please note that Class 38 includes telecommunications services, or those allowing one person to communicate with another by a sensory means. On the other hand, computer system administration for others, computer system analysis, computer system design services, and various other computer related services are classified in Class 42.
As a final comment, while it is not clear from the facts whether you stand a good chance of getting your mark registered, the USPTO can only refuse registration. It cannot require a party to stop using a given mark. This can only be done by way of a lawsuit filed by one party against another. One risk you might take in filing an application is that this could put you on the other party's radar. This is especially a concern if the other party's use predates your use of the mark.
If you wish to file an application and/or further analyze the overall issues involved, I suggest you retain experienced trademark counsel to review the matter.