Hello Ashok,
First of all please make sure SAP system is running fine. For windows OS, please check you have green light in MMC and for unix please execute "sapcontrol -nr <instance number> -function GetProcessList" to see the status of each sap processes.
In case there is no any problem with SAP system, then we try some efforts with SAP Logon.
1. create a new entry to NSP in SAP Logon with Application server instead of message sever (group logon).
2. if 1 works, check you have correctly maintained sapmsg.ini.
3. if 2 has no problem, check hosts and services files have been correctly maintained. The files are located in C:\Windows\System32\drivers\etc.
Hope the information is helpful.
Best regards,
Yuki