I've got the same problem with my ePO 4.5. I have already checked my DNS and any other detail that could make it fail.
Well, if anybody sorted it out, please help me!
You should make exception or disable Firewall on remote computer.
Also, if you want to use Agent Handler, you shuold switch SQL server from Windows Authentication to Mixed (Windows and SQL Authentication), create new SQL account with appropriate rights.
Then you need to reinstall Agent Handler using SQL authentication.
The ping command built into the EPO console relies on the IP address last reported back by the agent (so it does not use the hostname for a DNS lookup). If the machine is unmanaged then it has no IP address listed in its system properties thus the Failed to determine host IP address error.
I suspect your agent push problem lie elsewhere. KB56386 may help you determine where the failure is:
You can also review the server task log (menu | automation | server task log) for clues as to why the push is failing. Finally if you require further assistance then grab a copy of the epoapsvr.log (<ePO install directory>\DB\Logs\epoapsvr.log) if your using ePO 4.0 or the server.log in that same directory if your using ePO 4.5 immediately after failing a push and post the log and the name of the machine(s) you failed the push to.