To me it sounds like a loss, broken, or corroded wire in the power system. The big 3 will upgrade and replace these wires. Being you added "my new system" to which I hate that name for a car stereo.
When you add high draw electronics or light upgrading the factory wiring is needed as are no fuses in these wires. While a bit extreme the potential for overloading them and melting wires is there. So upgrading with 4awg will get the job done, some will say it is not needed unless you have a hi po(anything over 95 amp) alternator. Since you have issue already and a car stereo you need the big 3.
Which is just installing 4 awg wire from alt to batt, engine to chassis, and batt to chassis. Pretty simple but it is the backbone for power distribution for the entire truck.
99 x-cab 4x4 4.0l auto
mods, cranked t-bars, silencer delete, k&n drop in, Rebuilt trans ,Trans Go stage 3 shift kit, 3200stall Fuddle Racing Torque Converter,
VANIR 63mm TB, Roush split rear exit exhuast, E-Fan, JBA Headers
Auto up/down both windows, OHC, EATC (soon to be modded)
03 Crown Victoria Police Interceptor