Boost Voltage and Current in a Circuit
Not only in electronics, but in physics, chemistry, biology and thermodynamics (to name a few), energy is conserved. That is, you cannot make a device or process which will take in a certain amount of energy and produce more than that. There are a few, specialized exceptions, such as nuclear reactions, but these can be handled properly.

In electronics, power is current times voltage. You have not specified your output waveform, but I assume you want a constant voltage and current out. If this is so, then your input (4.8 volts times 2 amps, or 9.6 watts) is less than your desired output (5 volts times 3 amps, or 15 watts). Therefore, what you want is simply impossible, which explains why you haven't had much luck. Note that, if you could do it, you would have a perpetual motion machine, and you would become fabulously wealthy and the recipient of the Nobel Prize. Maybe even more than one.

If, on the other hand, you only want to provide your 5 volts and 3 amps for brief periods of time, it is certainly possible to use an intermediate energy storage device such as a battery. In this case, your input would charge the battery more or less continuously, and the battery would be connected to a DC-DC converter to provide 5 volts/3 amps intermittently.