The remains would mummify, petrify, erode, and eventually become just another mineral layer.
Where water is available the organic remains will dissolve and be replaced with inorganic minerals to form fossils, and if no water is available the remains will desiccate and be preserved as mummies.
There wasn't much specification regarding the timeline or location, so the below are just the general process that will occur over a long period of time.
Mummification: In particularly dry areas like deserts or mountain peaks, the remains would mummify, much like this creepy fellow. Even with regular decomposition mummification can still occur naturally, so without scavengers and bacteria getting in the way much of the life in dry areas would desiccate and mummify.
Petrifaction: In areas with water, the remains would petrify. Water would leak into the pores of tissue and bone, and minerals within that water will precipitate out and saturate the remains, resulting in a combination of organic and inorganic remains. This process is called permineralization, and is the reason we have dinosaur fossils. Without bacteria, the soft tissue remains would also go through this process and become fossilized.
Over time, much of the organic remains would slowly be dissolved by water and replaced by minerals, in the uncreatively named process of replacement. Unless the fossilized remains reach a dry area, they will eventually lose all of their organic components and be no different from oddly shaped rocks.
Erosion into Mineral Layers: As explained above, the organic material in the remains will slowly dissolve and be washed away by water(and probably other chemicals). The dissolved bones, shells, beaks, and corals of the trillions of dead will pile to form layers of limestone, rainforests will turn into vast swaths of coal, fossils and mummies would be formed in amounts to put previous extinction events to shame, and the swarms of dead ocean critters won't even get to become oil without bacteria. If given enough time, even the petrified and mummified remains will erode like an other rock, leaving little evidence of life except layers and veins of organic minerals.