Award Bios Beeps mean....?

The only AwardBIOS beep code indicates that a video error has occurred and the BIOS cannot initialize the video screen to display any additional information. This beep code consists of a single long beep followed by two short beeps. Any other beeps are probably a RAM (Random Access Memory) problems.

Though I also found this:
One long beep then machine shuts down - faulty, improperly installed
or missing CPU
1 long - 1 short(Beep) DRAM ERROR
Four beeps then machine shuts down. This is because this version of
the BIOS will shut down your machine if no fan tachometer signal is detected
on the fan header. Make sure you attach a fan to the FAN1 or FAN4 header or
clear CMOS to reset to default (no checking).

If it ain't broke, etc.

Apart from the above, 1 long and 3 short beeps mean there is no video card or bad video memory.

Here re all the Award beep codes:

http://bioscentral.com/beepcodes/awardbeep.htm

I am leaning toward a minor flaw or ?quirk? to your fan which is cutting off sooner then possible that is causing an over heat beep.
If replacing the fan didn?t remove the beep, then towards your bios or motherboard, (You stated that you replaced the RAM) although it could be one minutely damaged DIMM set may be compatible and operational on startup and during usage. Yet, on shut down you here beep codes, this would lend to a tiny flaw on one of the DIMM sets (or on mobo/bios, etc?), or a minuscule incompatibility of the two, three, or four DIMMs installed. Try reseating one DIMM, shut down twice, and listen for the beep code, if all your memory sets have a beep error on shut down then were back to the mobo, bios.
If your; not pulling the plug every time to shutdown, or getting unsafe shutdowns, or long boot ups, then I wouldn?t worry about it.

1 Short DRAMS refresh failure.
2 Short Parity circuit failure.
3 Short Base 64k RAM failure.
4 Short System timer failure.
5 Short Process failure.
6 Short Keyboard controller Gate A20 error.
7 Short Virtual mode exception error.
8 Short Display memory Read/Write test failure
9 Short ROM BIOS checksum failure.
10 Short CMOS shutdown Read/Write error.
11 Short Cache Memory error.
1 Long, 3 Short Conventional/Extended memory failure.
1 Long, 8 Short Display/Retrace test failed.

Award BIOS beep codes

Award says that any beep patterns other than "one long followed by two short" are likely problems with the system memory. However, of late they have started adding other beep codes to their systems as well.

Recommendation:

If you have recently flashed the system BIOS on this machine and corrupted the BIOS, and the system supports the boot block feature, the beeps may be codes communicating the status of the system as it tries to recover from the failed flash procedure. This is especially likely if the floppy drive is accessed very early in the boot process.