How can I detect if this dictionary key exists in C#?

You can use ContainsKey:

if (dict.ContainsKey(key)) { ... }

or TryGetValue:

dict.TryGetValue(key, out value);

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Update: according to a comment the actual class here is not an IDictionary but a PhysicalAddressDictionary, so the methods are Contains and TryGetValue but they work in the same way.

Example usage:

PhysicalAddressEntry entry;
PhysicalAddressKey key = c.PhysicalAddresses[PhysicalAddressKey.Home].Street;
if (c.PhysicalAddresses.TryGetValue(key, out entry))
{
    row["HomeStreet"] = entry;
}

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Update 2: here is the working code (compiled by question asker)

PhysicalAddressEntry entry;
PhysicalAddressKey key = PhysicalAddressKey.Home;
if (c.PhysicalAddresses.TryGetValue(key, out entry))
{
    if (entry.Street != null)
    {
        row["HomeStreet"] = entry.Street.ToString();
    }
}

...with the inner conditional repeated as necessary for each key required. The TryGetValue is only done once per PhysicalAddressKey (Home, Work, etc).

What is the type of c.PhysicalAddresses? If it's Dictionary<TKey,TValue>, then you can use the ContainsKey method.