Try this:
pts = {{}, {}, {{t1, a1, b1, c1}}, {}, {{ti, ai, bi, ci}}}
(* {{}, {}, {{t1, a1, b1, c1}}, {}, {{ti, ai, bi, ci}}} *)
pts /. {} -> Nothing
(* {{{t1, a1, b1, c1}}, {{ti, ai, bi, ci}}} *)
If you have there nested empty lists you will need to apply the procedure several times. For example, let your list be:
pts = {{{}}, {{{{}}}}, {{t1, a1, b1, c1}}, {}, {{ti, ai, bi, ci}}};
Then the repeated application of the above rule can look as follows:
FixedPoint[ReplaceAll[#, {} -> Nothing] &, pts]
(* {{{t1, a1, b1, c1}}, {{ti, ai, bi, ci}}} *)
Have fun!