That board has an Award BIOS.
Beeps endlessly repeating indicate a RAM problem.
You link to a different topic, but apart from Award BIOS and RAM issues, there are no similarities. This motherboard has an Intel i430VX chipset, the other one has a SiS5598. As already stated, your i430VX chipset cannot run with a single SIMM (SiS 5598 can iirc, with disasterous performance though) and your i430VX is a very early SDRAM chipset (the first, in fact) with extremely limited compatibility, where the SiS5598 is a nice compatible 2nd generation chipset that will accept most DIMMs, worst-case only detecting/utilizing half the amount of memory.
So: your pic shows a single SIMM in SIMM slot 3. Remove it and put two matched SIMMs in slots 1 and 2. If that doesn't work, put the same matched SIMMs in slots 3 and4. If you have a 16 or 32MB SDRAM DIMM with resp 8 or 16 chips, you can try that in one of the DIMM slots (with no SIMMs present!) as well.
Still keeps failing? Then look at the cache. There is a COAST module in there. It might be bad (or incompatible). Remove it, then repeat tests with two matched SIMMs.
As for the Dallas RTC... I *have* seen boards refusing to boot with bad RTC battery, but they don't give bad RAM beeps like this one does. You need to mod or replace that DS12887A for the board to keep time and BIOS settings, but I strongly doubt it's the cause of not booting at all.
And for future reference: it helps a *lot* if you tell us exactly which SIMMs and DIMMs (brand+model if available, if not at least the form factor (72p SIMM vs 168p DIMM), number of chips and the chip code (first row of characters on the chips) you've tested and which slot(s) you put them in. Says a lot more than "I tried changing around ram sticks"