plzhelpherstart

ok guys i have a 95 miata that i bought about a month ago not running from an old lady. i have new fuel pump relay but i have to use the diag box to get it to cut on. new plugs that i have tested and all have spark. engine cranks strong but will never start with that being said i have done a compression test and the results with a cold engine are #1 120 #2 90 #3 90 #4 120 i am frustrated and have no idea what direction to go