No heat inside car.The core is new, the radiator is one year old, and the water pump is one month old.

I WENT 50 YEARS NO A/C. EVEN AT 110F . EVEN 1 YEAR OLD.
LOTS OF CAUSES. IF TRUE.
BUT NOT ONE WORD OF PROOF IT IT DID
220F IS NORMAL AND AF DOES NOT BOIL UNTIL 255f.
SHOW PROOFS?
1: NOT RUNNING CLEAR MIX OF 50% AF IS TOP CAUSE
17 YEAR OLD COOLANT IS NEVER EVER GOOD
NOR RUNNING ONLY WATER NOT ALLOWED.
2 BAD RAD CAP , REPLACE IT,
3: COOLANT TOO LOW (EACH MORNING COLD , CAP OFF ALWAYS FULL.
4: BAD THERMOSTAT AGAIN 16 YEARS IS NO GOOD.
5: LEAKS COOLANT TO GROUND, INSIDE ENGINE OR TO PASSENGERS TOES (FOOT WELLS) IS BAD.
6: WATER PUMP BAD, RUSTED OUT IMPELLER.
7:FAN BELT LOOSE. SLIPS. TENSION-ER BAD.
8: BAD FANS, DEAD OR OLD AND SLOW.
OR SIMPLE STUFF THE CORES BOTH CONDENSER AND RAD ENGINE ARE PACKED UP IN BUG GUTS.
SO BLAST THEM OUT WITH WATER HOSE SPRAY NOZZLE.

OR GET THE CAR SERVICED IN A REAL SHOP.
THEY DO KNOW WHAT TO DO AND CHECK.

Overheating is caused by:
1. plugged radiator core
2. Wrong mix of water and coolant.
3. Low coolant level.
4. stuck thermostat
5. hoses collapsing.
6. Air lock in system
7. Bad fins on water pump.

What about the water pump if the water pump is working right there would be pressure somewhere.

Flapper door inside duct work most likely stuck open not allowing heat to come thru the heater core.

most likely heater core and to check if the water pump working..allow vehicle to warm up enough for thermostat to open and check for circulation in the fluid inside the radiator..if see it..water pump works.

Is the engine heating up on the temperature gauge?

It looks like you changed everything involving the hot water. When the engine is warm, you should be getting hot water going through the heater core. By holding each hose from the heater core you should feel heat from both hoses. I did not see a new thermostat listed.

You need to also have the ductwork under the dash moving correctly. If you find that the water lines from the heater core are both hot, then you need the (doors) or flaps in the ductwork to route the heat inside. I do not see that anything was looked at under the dash.

Why was radiator replaced?Did it have heat before ? If it was plugged, the heater core may also be plugged. Try flushing it with a water hose in both directions. I dont know why the botton radiator hose would be cold, the radiator should be a uniform temp and the air coming through the radiator should be HOT, when the engine is at operating temp. What condition was the old coolant? if it was rusty, the water pump may have lower flow than normal.

yes a bad water pump can keep heat from getting to the inside of the car. it circulates the water through the engine

Sounds like the heater core (a small radiator of sorts under the dash) is leaking or a hose going to it is leaking. If in a warm climate, you could bypass or block the heater hoses temporarily. Their only purpose is to make heat avail to interior of car. The 2 heater hoses either connect to feedthru's at the firewall or simply pass thru the firewall to the heater core. Every car I've seen has it on passenger side.

Peer up under the dash, it should be clear where it's coming from.