Got a three year old PC myself (or thereabouts - a Dell Dimension E520, C2D E4300 1.8GHz CPU, 2 GB RAM, Vista Home Premium 32bit).
I have an external LG (GSA-E10N) hooked up to it, and the drive's a workhorse, so I don't see any issue with your specs.
First thing to do would be to use Verbatim, as Kerry suggested - both for SL and DL use.
For SL burns, I tend to burn at 8x as a safe bet. For DL, depending on the disc's rated speed, either 8x/6x for 8x discs, and 4x for 4x rated discs - once again, similar to Kerry's suggestion.
My LG's pretty picky regarding media quality - your Memorex and TDK DLs wouldn't stand a chance on it, hehe - and not a failed burn with Verbatim, SL or DL, apart from the odd disc that was dodgy straight out of the pack.
BTW, just as an afterthought: my other external, a Samsung SE-S084C, is a sweet reader of deteriorated or dirty/scratched discs. Isn't so good with DL burning, though.