Hi Sunny
Are we talking about a Whale Gusher type of pump?
If so, it has a diaphragm, inlet flapper valve and an outlet flapper valve.

It doesn't need to be primed and should pump, lift and expel as it is, if in good condition.
If any of the mentioned parts are punctured, perished or not sealing the pump will not lift water.
The other cause (not likely) is a crack in the pump body itself.
So, disassemble again, remove diaphragm, open it like a dish, suspend it somehow and fill with water.
This will show you if it is leaking.
At the same time carefully inspect flappers for wear, tears or other damage.

If it is not a Whale type diaphragm pump, ignore everything I just said.

gary

Hi suny
Let us know how it works out, please.
If you do end up needing a new pump, this an option. I have one.
www.banggood.com/720GPH-Plastic-Diaphragm-Water-Pump-Manual-Hand-Bilge-Water-Pump-p-1022968.html?rmmds=search&cur_warehouse=CN

No removable handle and no replacement parts, but cheap and surprisingly good quality.
32mm hose connection.

Gary