Four megabytes is (just so) enough for 1600x1200 in TrueColor. What limits older cards isn't the amount of RAM, but most of the time it's the maximum pixel clock they can drive - particularly in TrueColor.
For 1600x1200 at 60 Hz you'll need about 160 MHz pixel clock; old cards often can do about 230 at up to HighColor (16-bit), but only have that in TC. Try and you'll see.
As has been said in every single one of the kerbazillion "Does my card support this resolution" threads, just pop up the "List All Modes" window after unchecking "Hide Modes this monitor can't display".