If you are using some kind of emulator you can try to capture the traffic using Fiddler (www.fiddler2.com). This is a proxy that shows you any request your made and you will find the HTTP rest url and a 401 as reply.
Possible solutions depending on the software your use:
- You could try to nagigate the "browser" inside of your application to show some kind of content from the sharepoint server. Try a picture from the sharepoint url. The "browser" normaly trieds to authenticate and will prompt the user to authenticate (depends on the platform). maybe you can change a setting of the "browser" that autnetication is allowed. After that authentication request you should be able top authenticate to the REST service.
- [EVIL] Switch to basic authentication (you MUST use HTTPS) on the sharepoint web application (maybe a special zone only for the app). Your rest request can be authenticated directly within the url: http :// firstname.lastname@example.org:1234Pwd@sharepoint.company.com/...
There might also be an issue with the type of authentication. If the mobile platform is only doing NTLM v1 and your company hopfully disallows this authentication (because it is insecure) you will never be able to access the REST endpoint. Try to get some kind of HTTP monitoring sofwtare between you (the app) and the server. Try fiddler or wireshark to gather more information about the problem.