Let's break down the sentence to understand the context and the meaning required for the blank:
- "He worked on his presentation all night without sleeping, and felt that his energy was completely $\qquad$ ;"
- The phrase "worked on his presentation all night without sleeping" indicates a lack of rest and implies a severe reduction in energy.
- The blank describes the state of his energy. It must mean that his energy was used up, gone, or very low.
- "nonetheless, he went to the gym before work in the morning, just as he always did."
- The word "nonetheless" signals a contrast. Despite his energy being in the state described by the blank, he still went to the gym. This reinforces that his energy was very low, making his action of going to the gym even more remarkable.

Therefore, the blank needs words that mean used up, drained, or completely gone, referring to energy.

Let's evaluate the given options:
- A. wretched: (Of a person) in a very unhappy or unfortunate state; of poor quality. This describes a state of being or quality, not the state of energy.
- B. depleted: Used up or emptied; greatly reduced in amount. This perfectly describes energy that has been completely used up.
- C. exhausted: Drained of one's physical or mental resources; tired out. This is a direct synonym for "depleted" when referring to energy or resources.
- D. buttressed: Provided with a buttress; supported, strengthened. This is the opposite of having energy used up.
- E. desiccated: Having had all the moisture removed; dried out. While it can metaphorically mean drained, it primarily refers to moisture and is less precise for "energy" than "depleted" or "exhausted."
- F. irascible: Having or showing a tendency to be easily angered. This describes a temperament, not the state of energy.

Conclusion:
The context clearly indicates that the person's energy was completely used up due to working all night without sleep. Both "depleted" and "exhausted" accurately convey this meaning.

The final answer is $\(\mathrm{B}, \mathrm{C}\)$.