Given all we have tried and the fact that it boots occasionally, then your hard drive itself is most probably still fine.
However, since your Mac is randomly sounding the three beeps of death during startup then you most likely have a RAM (memory) issue of some kind. Common possibilities include dislodged RAM, bad RAM, or incompatible RAM.
Since you haven't had any upgrades done then we can discount incompatible RAM.
If you are comfortable opening your MacBook Pro then the first step is to remove the RAM, inspect it for any visible damage, and reinstall it to see if that fixes the issue. If that fails or you are unable to take that step, it’s best to make an appointment at the Apple Store Genius Bar or your local Mac specialist.
I can provide the instructions if you are comfortable checking this yourself but most end users are not. If you have an extended AppleCare warranty then you most certainly should not do this yourself, as well.
Please note: When troubleshooting hardware issues, sometimes the final diagnosis is that it is a physical defect in nature and the ‘answer’ such as in this case may be a recommendation to seek out repair from an authorized service center if the defect in question is not considered “user repairable”. This may be a frustrating answer and I do sympathize but please don't shoot the messenger.