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ICMP packets (Ping) is normally blocked on firewalls by default.<br />
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When you have a computer set to allow remote connections to this computer enabled, the firewall exception to allow communication is automatically enabled. However, there are different types of networks: domain, public and private. When the setting Allow remote connections to this computer is enabled, the firewall exception for the domain network is enabled but not the exception for the Public network. If a machine isn't domain joined, then its network would be Public, therefore you'd need to perform the following to allow remote desktop:<br />
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&nbsp; &nbsp; 1. Log on to the computer.<br />
&nbsp; &nbsp; 2. Open the Windows Firewall with Advanced Security MMC snap-in.<br />
&nbsp; &nbsp; 3. Navigate to Inbound Rules.<br />
&nbsp; &nbsp; 4. Right-click Remote Desktop, User Mode (TCP-In), where the profile is set to Public and select Enable Rule. Repeat for Remote Desktop, User Mode (UDP-In), where the profile is set to Public.<br />
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You should now be able to connect.
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Are you also pinging by name or by IP address? Is it possible the IP address is different from the associated name on your DNS server?
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I manage IT operations for a company with over 30 branches. &nbsp;Occasionally a computer will lose it trust relationship with the domain and I have to rejoin it. &nbsp;The problem is that I have to walk someone at the site through the process because I can't ping or RDP computers that are not on the domain. &nbsp;Even computer that work properly and are not on the domain can't be pinged or RDP.<br />
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As soon as I join the machine to the domain everything works great. &nbsp;What is preventing me from accessing non-domain computers?
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I manage IT operations for a company with over 30 branches.  Occasionally a computer will lose it trust relationship with the domain and I have to rejoin it.  The problem is that I have to walk someone at the site through the process because I can't ping or RDP computers that are not on the domain.  Even computer that work properly and are not on the domain can't be pinged or RDP.

As soon as I join the machine to the domain everything works great.  What is preventing me from accessing non-domain computers?

Can't ping or RDP non domain computers.

The Domain Name System (DNS) is a hierarchical, globally distributed system responsible for associating the name of a computer, service or other resource into an IP address for connecting to the Internet or a private network. Most prominently, it translates domain names to the numerical IP addresses needed for the purpose of computer services and devices worldwide.

Networking is the process of connecting computing devices, peripherals and terminals together through a system that uses wiring, cabling or radio waves that enable their users to communicate, share information and interact over distances. Often associated are issues regarding operating systems, hardware and equipment, cloud and virtual networking, protocols, architecture, storage and management.

Networking

Network Management involves issues that are independent of specific hardware or software, including email policies, upgrade planning, backup scheduling and working with managed service providers for Desktop-As-A-Service (DaaS), Software-As-A-Service (SaaS) and the like through the use of tools, coupled with manufacturer standards, best practice guidelines, policies and procedures plus all other relevant documentation. Network management also includes monitoring, alerting and reporting, management reporting, planning for device or service updates, the backup of configurations, the setting of key performance indicators and measures (KPIs/KPMs), associated service level agreements and problem records as part of the IT Service Management (ITSM) framework.