What you are asking for is Holy water, and you are rejecting the suggestion that you use regular water. The only reason for preferring Holy water over water is religious. There are simple, randomly-seeded PRNGs that cannot be distinguished from true physical randomness by any known process. And these systems are non-deterministic.
A real-world computer has several sources of true physical randomness. For example, a modern x86 CPU has a 'TSC' which measures the instruction cycle count (and thus, indirectly, the time to a resolution of a billionth of a second or so).
You can capture the TSC when a network packet arrives. The low bits of the TSC will depend on the precise offset between the crystal oscillator that times the network interface and the crystal oscillator that runs the CPU. This is dependent on microscopic zone temperature variations in the two quartz crystals that are believed to be truly random.
Similarly, you can capture the TSC when data arrives from the hard drive. The low bits are dependent on turbulent airflow shearing between the hard drive surface and the case. This is also believed to be truly random.
Well-known algorithms, such as the one the Linux kernel uses (developed by Theodore Ts'o based on the work of M. Matsumoto and Y. Kurita) use the avalanche effect to convert a few unpredictable bits into a much larger number. The only differences between the outputs of these algorithms (assuming they are properly seeded by TSC data) and the output of true physical randomness is religious -- no known method can distinguish these outputs. There is no test that one will pass and the other will fail.
I have developed random number generators for online casino use that have achieved independent certification. These methods are the ones used in the real world.