Dell Inspiron 5100 (2003) with RAM issues (voltage, PSU suspect ??)

[13hm13]

Here's my device:
LAPTOP: Dell Inspiron 5100 (2003) 2.4Ghz p4, dual-boot: Windows XP pro, sp1 + LinuxMint ( LM 17.1 MATE ), with 128GB ssd, 512mb ddr sodimm.

The 5100 runs fine, even after 19 years of daily, gentle use, "always on", and on adapter power only.
HOWEVER, over the past 5-6 years there has been a restart-up issue (after power down or power loss --- I leave all my PCs/laps in daily use in ALWAYS-ON condition, even going months w/o re-boots, but the inevitable always happens) .
Seconds to few mins after pressing the power button to restart , the lap tries to get into BIOS, but the screen remains blank and laptop powers down automatically after 10 sec. Repeat power-button press a few secs to a few mins later. Same issue. HOWEVER: If I waited more than, say, 0.5 hrs to restart (like typical power blackout), start up NORMAL -- BIOS, Win startup, all NORMAL.
Looked into tho issue, and it was as I suspected, a memory module (RAM) issue. The short (10 sec) failed BIOS bootup I noted above does display a diagnostic LED fault code:
The Caps Lock flashes this code (see table in link below):
https://www.dell.com/support/kbdoc/en-us/000140521/a-reference-guide-to-the-inspiron-notebook-diagnostic-indicators#Prior_to_2006
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LEDs: Off Flash Off

Description: The memory is believed to be good but it is about to be exercised (such as when shadowing the BIOS and when testing / zeroing all memory).

Next step: Reseat the memory module(s); Contact Support

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HOWEVER, the lapse in time before the laptop re-starts normally has been getting longer (say 1 hr) .... up until a week ago when all I could get, even after hours of power-down, was the same flashing Caps Lock led.
I swapped memory modules and FINALLY got one (256 MB, lower than orig. 512MB) to work. But that 256 didn't want to start smoothly either (often with the same Caps Lock flash code). I have several other modules on hand. A 128MB works, but as far as I tested, nothing over 256.
It may be that the PSU circuits are getting old. Haven't opened up the 5100 yet (to look at the MBD), but I saw no electro caps from some online photos of the 5100 internals.

EDIT:
Whether re-boot attempts made from battery alone, or ac adapter (no battery) seems to make NO difference ... same issue.
May 2017, I replaced the orig. AC pwr adapter (20v, 4.5a) to a new one (19.5v, 4.7a) . I wonder if increasing the adapter voltage by 0.5v might now add enough juice to get higher-capacity memory modules t operate (or at lease make for smoother , more-reliable power-ups).
EDIT 2:
As I noted, I did install several other RAM sticks to test, many of them are new or very low hours.
About the LED code ... I provided a Dell link above. Dell does not indicate anything beyond what's in that table.
This lap top has TWO sodimm slots, A and B (each 266Mhz). Now, however, only SLOT B now works. I do recall SLOT A used to work.

[Rick Law]

This may NOT be your problem, but may be it is worth a look-see.

I have a couple of old laptops with similar symptom of needing to wait before start-up and doesn't stay up.  In my case it is fan/heat issue.  After being in use for a long time, the fan collected too much junk to keep the machine cool enough and it goes into thermo-shutdown.

The symptom it shows is just like what you described.  One of them, I changed the fan it is has been happy and ran until I finally upgraded it years later.    The other one, I run it with the lid open.  I have a PC (not always on) that also shown similar symptom - after ON for a while, it shuts down (or freak out) and wont get back on until a wait period.  In that case, I was able to apply more heat sink compound and it is still running.

[13hm13]

NO, No, No!!! The fan (still orig.) is cleaned and lubed once every 4 months. I also run a Speed Fan utility that monitors all critical temps that have internal RTDs (like the CPU, HD, etc). And ... I have a wired RTD - -that connects to my room Weather Station --  affixed to the bottom of the laptop.