Dim and "unblink" a pc power LED?
Total guesswork, but brightness is perceived logarithmically so the exact resistor values are not critical. 

You could try something like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

The 2200uF/6.3V electrolytic capacitor needs to be installed with the correct polarity. Eg. Nichicon UFW0J222MPD. 

If you don't like the way it works, change the values (perhaps in steps of 2 or 3:1, don't bother with much less of a change). If you're purchasing parts, get a few values- you can put resistors in series or capacitors in parallel to increase the values. 

The "attack" time constant is of the order of RC where R is 50K or less, and it will decay visually slower because the LED current will drop. 2200uF and 25K-50K is only about 20-40 ms so it won't make much difference turning on, but will seem a bit less abrupt turning on and especially going off. 

If you decrease the resistors to get more brightness you'll have to increase the capacitor proportionally to get the same time constant and you'll rapidly run out of practical sized capacitors. In such case it might be better to try just a single resistor.