help starting problem

i have a 97 with 153k onit and lately it has been having trouble starting. sometimes it cranks for a long time and other times it is like a dead battery and it just clicks. the wierd thing is that when it wont start the dome lights dont seen dim like they would with a dead battery. so is it the battery or may be my alternator?

Remove, clean, inspect for damage, and firmly re-install all the wires to your battery, alternator, and starter.

Have the battery load tested at a parts store or repair shop. The starter and alternator can be tested also.