Sublimation is cool but tricky. After verifying that you have true sublimation paper and no residual regular ink I recommend printing a solid black sheet then cut it into test strips about an inch wide by a couple long and do many test runs. Vary the dwell time starting well below what you think it should be and increase the time in 5 second increments. Pressure can have an effect but mostly with outgas along the edges and marks from the paper edges. You won't want a lot of pressure most of the time.
Temp check needs to start by checking your press with a temp gun in several places. Cheaper presses tend to have hot or cold spots. If yours is not even you probably won't get good consistent results. No one tells you when they sell you a printer that you also need a quality heat press, the cheap ones are often too unpredictable. If all the way through the timed trials your color stays brown then you have too much heat and need to back it down. This is assuming you have already established a consistent platen temp of around 400deg or whatever your ink supplier says to shoot for. They are not always gospel so you may find you have to reduce it. Again I recommend in small increments and work down from 400 5 degrees at a time. Use the recommended time whatever it is when dong this since the earlier time changes had no effect. If this still does not product the results you may have to take a look at the time tests and decide if one or two were better than the rest and combine the test doing both lower heat and also shorter time. You may tie up a whole weekend playing with this, I did.
If all these fail the next step is to play with your color profile and depending on your design program you will begin by doing various mixes of black. I recommend 50,50,50,100 to start with. When I did this I was working on orange and navy blue, two of which are really challenging to get to look good. I actually made a test page than had various CMYK mixes with the color combinations listed right beside the actual swatch so I could do a whole sheet at once and it helped immensely to keep track of what color was what. I then had to do the same test as you will have done on black and worked up through the time and then down through the temp. Never did find a navy that satisfied my client.
You will probably find your temp and or time to be off and once you dial it in most of the rest of the colors will also come alive.