If I am home alone, why do I have to be dressed modestly in order to pray?

Answer:

If prayer only involved G-d, nudity wouldn't matter. But prayer is also about you, the human, and nudity plays a factor in the human mind.

Adam and Eve were actually embarrassed of their nakedness, and hid when G-d came to the garden. Until they sinned life was only about G-d, and they were therefore not self-conscious about their own nudity. However, once they sinned the human mind emerged with its own identity, one that wasn't in perfect harmony with G-d. Man began to focus on his own desires rather that G-d's. Subequently, the human mind felt the need to conceal its body's nakedness.

Humans don't talk to other people while they are naked. The human mind does not associate the state of nudity with respect and awe. To the contrary, when have an important interview, or if we have to meet a dignitary, we get dressed and try to look our best. The human mind associates respect and awe with formal attire.

We must pray with respect and awe, and we must therefore pray in the appropriate attire.