RTC not keeping the correct time or date

[Castellen]

I am wondering if R803 should be left in the circuit, because electricity takes the path of the least resistance.

Where did you get that preposterous idea??  Electrical current flow takes *all* parallel paths, which is just as well because otherwise nothing electronic could ever work; these all contain multiple parallel paths of differing resistance.  Besides, R803 is part of a series circuit with respect to battery current flow, so either way is part of the only current path.  Its only purpose is to limit current flow into a NiCd/NiMH battery which is charged with a simple constant current concept.  Replacing this resistor with a diode just means the current can only flow from the lithium cell to the RTC.

It's perfectly legitimate to replace R803 with a small signal diode.

Here's the schematic of the A2000 RTC.

As I mentioned here you need to make sure the diode polarity is correct.  If replacing R803 with a 1N60, you need to make sure anode side goes to battery + and cathode (stripe side) to U801 pin 18.

Use a DC voltmeter to check you have >2.5V between U801 pin 18 and ground (computer chassis) with the computer off and the battery fitted.

[Castellen]

Not saving. I baught the CR2032 coin battery from Radio Shack. I noticed that many people use a 1N914 diode, I wonder if this would be a better diode to use instead of the 1N60.

The 1N60 diode you already have is fine.  In fact it's a better choice over silicon diodes for reasons I've already explained here.

You need to check that U801 has power (greater than about +2.5V) on pin 18 as supplied from the cell when the computer is powered off, else it's obviously not going to keep the time data.

If the save button on the time prefs program is ghosted, it means the system cannot see the RTC.  Almost always, this is a result of battery corrosion damaging tracks, vias and ICs.  I've written this repair guide which is for the A4000D, but may be partly helpful for the A2000.