Cessna 172 pilot reported having an intermittent alternator inoperative light during cruise at 6000 feet in IMC. The pilot was able to communicate with ATC via phone and hand held radio and land.

Narrative

Intermittent illumination of the 'Alternator INOP' light at 6000 in IMC; direct ZZZZZ intersection to join the ZZZZZ1 arrival into ZZZ1 airport. This light was monitored for the majority of the return flight; presumed to be an error with the light; since the other avionics seemed to indicate the battery was still charging. 30mi from ZZZ [airport]; an error presented itself on the G5 PFD (Primary Flight Display) which indicated it had lost communication with an air data computer (ADC) or some portion of one. Since we were already aware of the potential for an alternator issue we prompted ATC for a descent out of IMC and to amend our plan to an approach at ZZZ then to ZZZ2 [airport]. The PFD error was followed by an alert on the GPS that ADSB in and out had been lost. We were informed by ZZZ APP that we were no longer on their radar scope; not even a primary target. This was followed by other associated errors; and the battery dying which left only the PFD and HSI on their independent batteries. Communication was retained with ZZZ approach via phone and hand-held radio. We landed without incident at ZZZ.Prior to this incident; a new engine had been installed in the aircraft. The aircraft had approximately 13 hours since this installation of flight time.