1995 LS 400 slow start.....why?
 

My 95 LS 400 has been slow to start,comparatively.What I mean is when you start the car, it turns over for a few seconds,like 4 or 5, and then sometimes fails to start.I hit it the second time, 4 or 5 seconds again,and it starts.
I figured it was ready for a tune, so I ordered the parts,(dealer), and last night, installed new plugs,caps, rotors, and a wire set.
It still does not kick right off, like it was 25,000 miles ago.
It does have 164,000 miles, but the plugs were somewhat deposited, a little burnt, but even color, and no oil fouling.The caps had carbon arcing,and did not come off the plugs whole,(clips stayed with plugs on a few.
So I am sure cap and wires, rotors,were original.Plugs look to have been changed maybe once.It now idles perfectly, and runs like a bat.
Any ideas on my slow start?BTW,the battery is very good,I replaced with an Interstate about 2-3 years ago,(right size,spec, etc.).
Other thing is , the dealer says you don't need to change the fuel filter.They never do,and had not sold one.Is this right?
This Noob says THANK YOU!! Hope you can steer me right, and that this is an easily solvable problem.