Take all your problems and rip them apart:
If C2=R2 and D2 is < T2 then U2, if D2 is >T but T3 but < T4 then U4 if D2 is > T4 but < T5 then U5, if D2 is > T5 but < T6 then U6 BUT if C2 does not equal R2 then S8
Start with this using NA() to represent parts which haven't been completed yet (this will show the #N/A value in the cell):
=IF(C2=R2,NA(),S8)
Add the lookup based on D2:
=IF(C2=R2,IF(D2<T2,U2,NA()),S8)
Assuming that the next part is D2 > T2 and D2 < T3 (althought strictly this formula says D2 >= T2) and result is U3:
=IF(C2=R2,IF(D2<T2,U2,IF(D2<T3,U3,NA())),S8)
Now add between T3 and T4:
=IF(C2=R2,IF(D2<T2,U2,IF(D2<T3,U3,IF(D2<T4,U4,NA()))),S8)
Between T4 and T5:
=IF(C2=R2,IF(D2<T2,U2,IF(D2<T3,U3,IF(D2<T4,U4,IF(D2<T5,U5,NA())))),S8)
Finally between T5 and T6:
=IF(C2=R2,IF(D2<T2,U2,IF(D2<T3,U3,IF(D2<T4,U4,IF(D2<T5,U5,IF(D2<T6,U6,NA()))))),S8)
We still have NA() because you haven't defined the behaviour for C2=R2 and D2 >= T6
As Stobor said in the comment to your original question, using VLOOKUP would be much better - see http://office.microsoft.com/en-us/excel/HP052093351033.aspx for details
Your current structure in the T and U columns won't work with VLOOKUP because:
the next largest value that is less
than lookup value is returned
This would mean that VLOOKUP would return U3 when you wanted U2, U4 instead of U3 and so on. To solve this you would need to move all of the entries in the U column down by one row, put a dummy value or =NA() into U2 and create a value in T7 that was greater than the existing value in T6