If swapping the DIMMs over means the other DIMM works in the other slot, but putting both in always results in the one in the same slot not showing up, than you have a duff mobo. Might also explain the other weirdness.
In that case - bin it. Or it will like bite you in the ass sometime you really don't want it to.
Always install DIMMs with a grounding strap or with the machine plugged in BUT TURNED OFF AT THE SOCKET [keeps the metalwork grounded]. ALWAYS have bare arms, and cotton clothes, and don't move around more than your arms. Touch the grounded metalwork every 30 seconds, or better still rest a finger on it.
Remove the battery too, and wait a minute.
You may know these things, but if you don't you might fsck up the machine completely.