Assuming one day all the algae disappear:
A) ocean food webs would completely collapse. algae is the main driver of photosynthises and without it the basic energy inputs for the rest of the food webs would be gone, causing mass die-offs in the ocean.
B) similarly, the oxygen output is significant from algae (about half of total production, so life on land would suffer immensely and quickly (faster than if food production from the ocean ceased alone).
C) the death of other ocean organisms would cause the oxygen in the ocean to be used up as the organic material decomposes (this is the problem with algae blooms). This would lead to even less available oxygen for any remaining species, and an increase in CO2 levels adding to ocean acidification. I'm not sure it would wipe out all life int the ocean, but it would get close.
D) This is a guess on my part, but since there's no more algae to absorb the sun's radiation, all that radiation previously photosynthesized into sugars would now be hitting the ocean and would instead transfer their energy to water molecules, causing them to vibrate and raise the temperature of the water. (It may be that since plants mostly synthesize using visibile, specificaly blue and red, light, this effect could be negligable) For those in the ocean, the environment becomes even more hospitable, and for those on land, the additional ocean warming would likely cause greater climate shifts.
However you cut it, it would suck.
