Why aren't all objects transparent?

For an object to be transparent, the light must be emitted in the same direction with the same wavelength as initially. When light strikes a brick, some is reflected in other directions, and the rest is re-emitted in longer, non-visible wavelengths. That is why a brick is opaque to visible light.

Some materials we consider transparent, like glass, are opaque to other wavelengths of light. Most window glass these days, for example, is coated with infrared- and ultraviolet-reflective films to increase insulative capacity. You can see through these fine with your eyes, but an infrared-based night vision system would see them as opaque objects. Another example is that most materials are transparent to radio waves, which is why both radio broadcasts and radio telescopes are so successful.

You say:

For a non-transparent object like a brick, when the light is absorbed by an electron it will eventually be re-emitted.

but this isn't true. In a solid the excited state can decay by transferring energy to lattice vibrations instead of emitting a photon. This means the energy of the incident photon is converted to heat and the photon is lost forever.