Welcome Skyline.
When your bike fails to start, do you have lights? When you say "into steps it runs again", does this mean you can kick start it?
When the battery was replaced was it dry? Some batteries need electrolite put in when new, then a long slow first charge. If it is not done properly the battery will not work.
Do you have access to a volt meter? If so charge the battery to over 12V an see if it retains that over night as Tools said, then start the engine and increase RPM to over 3,000 RPM. With the meter on the battery connections and the engine speed increased, does it show near 14V?
81 Honda CB750C - Current Project
67 BSA Spitfire MkIII - Next Up (Full Resto)
81 Honda GL1100 - Bob / CafeĀ“
80 Suzuki GS750L - Bratstyle
72 Honda CB450K5 - Basket Case
73 Honda CB350F Cafe' (Gone but not forgotten)
Don't wait for opportunity to knock... kick the door down and drag the old harlot in!