The paper investigates the role of the exchange-correlation potential and kernel in calculating excitation energies from time-dependent density functional theory (TDDFT). Excitation energies of helium and beryllium atoms are calculated using the exact Kohn-Sham ground-state potential and two orbital-dependent approximations: exact exchange and self-interaction corrected local density approximation (SIC-LDA). The choice of the ground-state exchange-correlation potential significantly affects the absolute position of excitation energies, with orbital-dependent potentials causing a uniform shift of transition energies toward Rydberg states. The study explores three adiabatic approximations for the exchange-correlation kernel: local density approximation (LDA), exact exchange, and SIC-LDA. The results show that the exact exchange-correlation potential leads to more accurate excitation energies compared to approximate ones. For helium, the exact Kohn-Sham potential yields excitation energies very close to the exact spectrum, while approximate potentials introduce shifts. The SIC-LDA kernel provides better results than the LDA kernel, particularly for singlet and triplet states. For beryllium, the exact Kohn-Sham potential also yields excitation energies close to experimental values. The TDOEP-SIC kernel improves the accuracy of excitation energies compared to the TDOEP X-only kernel. The results indicate that the choice of exchange-correlation potential and kernel significantly affects the accuracy of excitation energies. The study highlights the importance of accurate exchange-correlation functionals in TDDFT for calculating excitation energies of finite systems. The results demonstrate that the inclusion of correlation contributions in the exchange-correlation kernel improves the accuracy of excitation energies, particularly for singlet states. The study also shows that the choice of exchange-correlation potential and kernel has a significant impact on the accuracy of excitation energies for both helium and beryllium atoms.The paper investigates the role of the exchange-correlation potential and kernel in calculating excitation energies from time-dependent density functional theory (TDDFT). Excitation energies of helium and beryllium atoms are calculated using the exact Kohn-Sham ground-state potential and two orbital-dependent approximations: exact exchange and self-interaction corrected local density approximation (SIC-LDA). The choice of the ground-state exchange-correlation potential significantly affects the absolute position of excitation energies, with orbital-dependent potentials causing a uniform shift of transition energies toward Rydberg states. The study explores three adiabatic approximations for the exchange-correlation kernel: local density approximation (LDA), exact exchange, and SIC-LDA. The results show that the exact exchange-correlation potential leads to more accurate excitation energies compared to approximate ones. For helium, the exact Kohn-Sham potential yields excitation energies very close to the exact spectrum, while approximate potentials introduce shifts. The SIC-LDA kernel provides better results than the LDA kernel, particularly for singlet and triplet states. For beryllium, the exact Kohn-Sham potential also yields excitation energies close to experimental values. The TDOEP-SIC kernel improves the accuracy of excitation energies compared to the TDOEP X-only kernel. The results indicate that the choice of exchange-correlation potential and kernel significantly affects the accuracy of excitation energies. The study highlights the importance of accurate exchange-correlation functionals in TDDFT for calculating excitation energies of finite systems. The results demonstrate that the inclusion of correlation contributions in the exchange-correlation kernel improves the accuracy of excitation energies, particularly for singlet states. The study also shows that the choice of exchange-correlation potential and kernel has a significant impact on the accuracy of excitation energies for both helium and beryllium atoms.