The starter does not work properly to turn over the engine. 

Either the new starter is bad, your battery is bad, or the cables are bad.

Posted by: @thom1628

what are chances that reman starter they sent is bad vs the cables now on top of that original starter I replaced and which cables would I be looking into.

There's a pretty good chance the reman starter is bad, it's not uncommon. The cables would be the battery cables. You can do a voltage drop test on them.

https://www.youtube.com/watch?v=qPpHRuddhh4

Try jumping to another car. That would eliminate the battery. It is possible you got a bad starter. Turning the crankshaft with a wrench is a good idea to verify the engine is free to turn.

Posted by: @thom1628

how can I test if its still good

https://www.autozone.com/lp/free-parts-testing

Well the last starter I took out was not engaging at all and solenoid would just click and would not engage with flywheel at all.

I got it tested and that starter was bad. Battery tested as good, what are chances that reman starter they sent is bad vs the cables now on top of that original starter I replaced and which cables would I be looking into. Thanks much! 

Have you tried turning the engine with a wrench on the crank bolt to make sure that there is no binding due to a flaw in the installation? If the voltage drop test passes, next option is to just pull it out and bench test the starter, or If you can, take it back saying it's defective. Also, when doing the voltage drop test, make sure the battery voltage (at the battery) stays in the "good" range. No lower than 9.5V, I'd say.

Thanks everyone for all the help. and  for chiming in I really appreciate it and need expertise on next steps as I have an update.

After jumping the car it finally started. However, it took a hell of a lot of effort to get it started. It would not start until voltimeter read 13 Volts. I let the other car run for a little over five minutes before trying to start mine and it still took a few good Attempts before it successfully started (only when battery read over 13/ 13.01 V did I have success) - after turning the key for a good 10 seconds the car finally started. As it was starting up the battery voltage never fell below 10 V.

Unfortunately, i got it started up at a cost...the serpentine belt began smoking and the rubber belt split/broke. After I disconnected the jumper cables and took the belt off I wanted to see if the car would still start. So started very briefly.. (on for 2 secs) It started without any issue. But after 15 minutes it wouldnt start up again.. voltage was about 11.7 when no longer starting

The battery only has 500 CCA, (51R) In fact, many  Accord owners of my gen recommend upgrading to the 24F battery type as it fits well with similar demensions  no modifications and 725CCA. (125 more than stock battery)

My thought was that perhaps the battery does not have the full cold cranking amps to consistently start the car. After removing the serpentine belt I noticed that all the pulleys are able to spin by hand except for the alternator and the crankshaft pulley. Are either of these pulleys "Supposed" to be able to spin by hand if the car is not running? 

Based on my update I am hoping to get help on what direction to go. Can a battery still test as good but not be able to live up to its CCA? What is the likely cause for belt smoking and splitting - seems like something might be seized up. Good news is car was running so  starter is able to engage. I shut off car and didnt drive to see if alternator would fully charge  battery because no serp belt to throw on.

I worked outside for another 90 min or so and battery was at still at 11.7v, only seemed to lose charge after  successful start up and  then 2 brief tests to see if it still started after I took the belt off -

I would really appreciate any perspectives on the matter. Thank you!

Tom

The alternator should spin freely by hand.  The crank will need some force to turn with a large wrench.  For sure, from your description, the alternator is frozen.  Thus the burnt belt.  Without the alternator spinning your battery won't charge.  Thus the low voltage after cranking.

Hi,

So I was able to loosen the alternator pulley with breaker bar and no longer seized .. spins by hand now and moves when car starts. Belt is coming tomorrow. Without removing the alternator from the car, how can I test if its still good with belt off? Any way to test with voltmeter? Or any other helpful suggesions? thank you so much!

Got the belt on, but never got to test voltage- even though I got the alt pulley loosened as soon as i started car alt pulley failed to spin and new belt started to smell like burnt rubber. Is this likely a bad alternator or other part that might need replacing like the bearing ? 

Thanks!

I ordered a new serp belt and while waiting hooked up my float charger.. battery got fully charged and maintainted 12.6 V for over 24hrs.

Yesterday got the new belt on and it started right up, but alternator pulley failed to spin and rubber smell began again so shut off immediately. Any ideas ? likely new alt needed or perhaps bearing? I have seen a video with a guy suggesting to put oil into the alternator as the prob causing seizing alt is likely the stator.

I didnt want to do that yet as I dont want to risk messing things up more until I got some other feedback . Anyone ever use this technique? thank you so much for all the help and expertise..

https://www.youtube.com/watch?v=W0_NwGwyWyk

Goodness, gracious, great balls of fire!!!  Replace the alternator already.  You're wasting your time trying to jiggle the alternator free, only to lock up and burn the belt again.  Either that, rebuild it.  Since you force the blockage free with a prybar, you could have caused some internal damages.

Thank you, anything I could do that would provide any info at all on its condition and perhaps offer evidence whether it is bad or still good? even if it it is not the proper way?