Installation of NetBackup Java Administration cpnsole is faled with error: Error 1719.The Windows Installer Service could not be accessed.

As suggested in the error you need to reinstall the MSI installer. I have done it many times and it works. Just remember that it requires a reboot.

http://www.microsoft.com/en-us/download/details.aspx?id=8483

Thank you, but system requirements for this package are:

• The Windows Installer 4.5 redistributable can be installed on Windows XP Service Pack 2, Windows XP Service Pack 3, Windows Server 2003 Service Pack 1, Windows Server 2003 Service Pack 2, Windows Vista, Windows Vista Service Pack 1, and Windows Server 2008 in X86, X64 and IA64 flavors.

And My OS is Windows 7.

Bottom line is:

You have a Windows Installer problem.
Have you tried to search Microsoft Support site for latest Windows Installer for Windows 7? 

I found the following on Microsoft: http://answers.microsoft.com/en-us/windows/forum/windows_7-system/error-1719-windows-installer-service-could-not-be/a3d7a90f-5953-4b93-a536-d807e21e0b93

and the following in https://support.microsoft.com/en-us/kb/315346 :

For support for this issue on Windows 7 and Windows Vista, see Microsoft Knowledge Base article 2642495: Error “The Windows Installer Service Could Not Be Accessed” when installing or updating programs on Windows 7 or Windows Vista

Hello, Marianne.

Thanks for your reply. I've tried to use all of recomendations that offered in your topics but it hasn't solved my problem.

Can I know if it's possible to install this version of NetBackup to Enterprise Windows 7 x64?

Symantec NetBackup Server
for Microsoft Windows
Version 7.0
December, 2009

Yes. Windows 7 Ultimate is perfectly supported. See the OS SCL:  http://www.symantec.com/docs/TECH76648

I have a Windows 7 x64 laptop. I have installed NBU 7.0 and in the meantime upgraded without any issues.

Important to check requirements in NBU Installation Guide, e.g. you need to have local admin rights, disable UAC, etc.
Depending on security levels enforced by your AV, you may need to disable this for the installation.