Does loss of dopaminergic neurons totally eliminate voluntary muscular control?

Suppose that someone has completely lost the ability to voluntarily control his/her muscles due to the destruction of the brain's dopaminergic neurons in the substania nigra

This is not correct. The substantia nigra plays an important role in both reward and movement. The degeneration of dopaminergic neurons in the substantia in Parkinson’s disease leads to loss of fine motor movement (leading to limited movement and tremors) and some loss of non-motor skills (loss of smell).

What locations control breathing?

The autonomous regulation of breathing is controlled by bundles of neurons called the dorsal respiratory groups (DRG) and ventral respiratory group (VRG) that together make up the medullary respiratory center. Source.

Though the exact mechanism of how we control our voluntary breathing is still a debated. We have a general idea:

Voluntary control of breathing is mediated primarily via the corticospinal and corticobulbar tracts and is important in activities such as speech, singing, and voluntary breath-holding. Disorders involving this mechanism occur mainly in bilateral pontine infarctions and lesions involving the pontine tegmentum that interrupt the descending motor pathways. - Neurology and Clinical Neuroscience, 2007

Would that person be able to breathe manually if he/she so wished, or would he/she only ever breathe autonomically?

Although the exact mechanism for voluntary breathing is not fully understood, the voluntary process is controlled by a series of nerve bundles. If the nerve bundles were severed, there would be decreased voluntary control over the breathing process. Losing the ability to manually breath could be bad for overall health. One study has found that a lack of the ability to manually breath can lead to poor spinal stabilization and posture.

What if you lost autonomous control?

There is a rare disorder known as central hypoventilation syndrome (CHS) that results in respiratory arrest during sleep (also known as Ondine's Curse). This disorder is caused by a lack of development of the neural tube (aka Medulla and the VRG/DRG) during birth or some type of traumatic brain injury. Treatment for this disorder is a lifetime of mechanical ventilation.