Question

What vital means of communication connected baltimore to washington, d.c., in 1844?

Answer 1

The telegraph

Samuel Morse sent the first telegraph message from Washington DC to Baltimore in 1844.   The message he sent said, "What hath God wrought?"

Within a decade, thousands of miles of telegraph cable lines were in use all over the United States, and then by the 1860s a transatlantic cable connected the USA to Europe for communication.