The flashing of the N and D light is actually just the N light flashing (Causing the D light to go out). This is indicating a trouble code is stored in the TCM (transmission side of the computer). Knowing that a fault is stored there, they best thing to do first is going to be to get the transmission codes scanned (this requires a dealer or professional scan tool; auto parts store scan tools can not read the TCM codes) just in case there is something out of left field going on there.
More than likely it is just going to be a ratio fault (the difference in speed between the two shafts in the transmission do not agree with the calculated ratio)... this is more of an afterthought to the failure though (you rev the engine and it doesn't move, eventually a ratio fault will set).
With the knowledge of the gear shift getting stuck combined with the worn out fluid, it is most probable you are going to be dealing with an internal failure here. Specifically, when you operate the shifter it moves a manual valve inside the valve body.... 99% of the time if there is any difficulty with the gear shift getting stuck, it will be debris caught in the manual valve. It is possible to be cable related, but extremely rare by comparison (plus that rarely ever goes away, whereas the manual valve often frees up after sitting or running for a period of time).
If there is nothing noteworthy with the trouble codes in the TCM, then your best course of action would be to get the fluid flushed out first with fresh SPIII and compare behavior.... while unlikely to "fix" the issue based on my experience with these, the next step moving forward would be hydraulic pressure tests which require good fluid to get accurate results, so you will end up at that point anyway.
Again from my experience with these... you will move likely be looking at debris in the manual valve or regulator valve, probably as a result of a broken wave spring or loosened drive nut. Those are the most common failures on the 40/50 series transmissions. Getting the TCM scanned about that flashing N light should still be priority though just in case there is something unusual going on that would shift our opinion any.