It showed 20.0 after I hit 4 Enter 5 *. After that, I pressed the buttons you told me and it gave me the same message. 01- 31 PRGM.

Okay, that's really weird. It looks like when you try to enter the programming mode, it doesn't go. So it's just executing everything in the run mode as you press the keys. Then when you press P/R to go back into the run mode, THAT'S when it enters the programming mode. That's super weird.

The first time you press P/R to enter the programming mode, PRGM should show up in the display to show that you are in that mode. Then when you go back into the run mode, the indicator should go away. You should be in the programming mode when entering the program, and then back in the run mode when you go to run the program. If you're doing everything right, then I'd be interested to see what it does as you do it. Other than that, I'm fresh out of ideas.

I tried it one last time, and it worked! What should I expect after it solves the equation?

Sweet! You must have had some accidental discrepancy between the programming and run modes. Maybe in the very beginning it was already in the programming mode, and you thought you were in the run mode, and vice-versa.

The calculator should be stopping every second or so to show the current calculated value. There is no "solution" per se - how Leibniz's formula works is that the calculator keeps calculating it over and over and over, getting a little more accurate each time. You should be able to see this every time is pauses. It should get to 3.1 in a few seconds, 3.14 in a few minutes, and 3.141 in a couple of hours. Hopefully it's pausing between calculations?

You can press R/S at any time to stop the program.

Yeah, it's pausing. I had to take the "running" picture quite a few times. I forgot to push f 9, so will it eventually get to 3.141 or 3.1415?

4 decimal places, so 3.1416 (since it will round up from 5). You can press R/S to stop the program, press f, 9, then press R/S again to resume the program. Although it would take several days to get to 4 digits! Leibniz's formula, as well as all other formulas to calculate pi, converge extremely slowly. My graphing calculator only gets to 5 or 6 digits after a few hours.

Oh, is that a flashing star at the bottom-left of the display? If so, that means your batteries are low. These are known to go over 20 years of regular use on one set of batteries, so I wouldn't doubt yours is still running on the original factory batteries.

Yeah, it started the low battery thing shortly after the calculation started. If you look back to the second picture, the low battery symbol is not there.

I (reluctantly) bought new batteries for this thing today. $4 a pop at your friendly neighborhood Radioshack. It cost $13 to buy batteries!

Ouch! Yeah, button cells are getting expensive. I payed $5 for one at Walmart a couple of months ago. I haven't checked, but I wonder if you might get a better deal at a dollar store.

My TI-1025 just showed its first sign of life since failing. When I put a battery in, the display showed EEEEEEEE (the overflow signal), with each digit of varying degrees of brightness. Then after a few seconds it just went blank, and that was it. The chip is seriously screwed up.

There's a "moon landing simulator" game which I recently discovered that I like playing on the 33E. It requires a couple of functions that the 12C doesn't have, but I managed to port it to the 12C last night. Of course, AFTER an hour of figuring it out, I found that someone already posted a 12C version online. Oh well, it was fun to figure out. Do you want to try it? I ask beforehand because it will be a pretty long post with the code and the instructions of how to play it...

A moon landing simulator? What in the world is that? I guess I could try it on the 12C if it won't run those batteries flat.

Nah, you'll get a decade or two out of those batteries.   It's a neat program that's based on real physics. You're in a spacecraft falling downwards toward the Moon. Your objective is to use the limited amount of fuel you have to land. You need to burn the right amount of fuel at the right time such that you land slowly, but don't run out of fuel before you do.

Note that I've put line numbers to the left of the functions - you see these line numbers on the left side of the display as you input the program. That way you can see where you are.

01   f 4
02    RCL 0
03    EEX
04    4
05    ÷
06    RCL 1
07    0
08   x<>y
09   x<y
10   GTO 20
11   R DOWN
12   R DOWN
13   STO 4
14   R DOWN
15   R DOWN
16   RCL 4
17   x<>y
18   +
19   GTO 27
20   R DOWN
21   R DOWN
22   STO 4
23   R DOWN
24   R DOWN
25   RCL 4
26   -
27   R/S
28   RCL 2
29   x<y
30   GTO 50
31   R DOWN
32    STO - 2
33   5
34   -
35   STO 3
36   2
37    ÷
38   RCL 0
39   +
40   RCL 1
41   +
42   STO 0
43   0
44   x<>y
45   x<y
46   GTO 61
47   RCL 3
48   STO + 1
49   GTO 02
50   RCL 1
51   ENTER
52   *
53   RCL 0
54   1
55   0
56   x
57   +
58   SQRT
59   CHS
60   STO 1
61   RCL 1
62   f 0
63   GTO 00

Before running the program, you need to store your initial height, vertical speed, and amount of fuel in storage registers 0, 1, and 2 (do this in the Run mode). The defaults are 500 feet high (500 STO 0), falling at 50 feet/sec (50 CHS STO 1), and 120 units of fuel to use (120 STO 2). When you run the program, it will show your initial vertical speed and height as a single number. For example, the initial state is -50.0500, meaning 50 feet/sec downward and 500 feet high. Then you key in how much fuel you want to burn, and then press R/S again. Burning 5 units of fuel will keep your speed constant. You can see how much fuel you have left at any time by pressing RCL 2. Then you can press R DOWN to see your speed and height again. When you land, or if you run out of fuel, the program will end by showing you how fast you hit the ground. There's no definitive "win" or "lose" values, but according to HP who originally wrote the program, anything faster than 5 feet/sec would probably spell doom.

What can I expect to happen after I (by some miracle) get all the information programmed into the calculator? Is it one of those games where, unless you pay constant attention and push all the right buttons, you die a fiery death?

No, it's not time-based. Every time you enter an amount of fuel to burn and press R/S, it will update and show you your current speed and height, and then it will just wait for the next input. Nothing happens while it's waiting.