Folks a client need a website where a ticketing system will be added to his existing website with a client base where client's networking setup will be added.
The clients will be able to login to their accounts and submit tickets for problem issues as well as the site owner to check out the clients network setup and a big MAYBE add some kind of remote system vpn or whatever to troubleshoot some of his clients problems.
Any recommended software, scripts, or whatever to implement such a system?
Welcome to WebmasterWorld drdave :) Are you looking for a technical-support ticket system (logging computer/network errors and such)? If so, you could try something like OTRS [otrs.org], there are versions for most popular Linux/BSD variants.
As for a remote vpn or login, it depends on the clients that you need to log into - are they on the same corporate network or similar? If so, there are several remote management systems available. If you are talking about the general public, it's virtually impossible as you would have to contend with a heterogeneous environment and having to debug access over a myriad of internet connections, home firewalls and routers.
The need for integration with the ticket system is not a requirement in my book - assuming a homogeneous corporate network of a size significant enough to require a ticket system for user bug reports, in most cases the remote management tools are already in place. The ticketing system merely needs to request a machine name when submitting the ticket, and the sysadmin can connect to that specific machine. I don't use such tools myself as I'm not involved in any sysadmin roles so I can't make any specific recommendations.