MacBook Pro 13" extremely slow, help!

Question

I bought the mac last summer (2012) and it's been flawless up until a short while ago. It's an i5 with 4gig ram and 500 HDD.
Of the two USB ports, the one closest to me stopped working less than a month ago (this is not the issue I want help with though, just mentioning it as it might be related somehow). A week later, I upgraded to Mavericks and everything remained the same. Computer was fine (except the usb port), then one night the computer crashed while I was using a music production program (which I've been using daily since I got the mac).
This is when the mac started going slow.
Starting the computer up now took 4-5 minutes and there was no point trying to open an application. I managed to back everything up (though it took about 15 minutes just to select all files, then two-three hours to move them to the external drive) and started the process of reinstalling OS X. I formatted the drive, which was a fairly quick process. Installing OS X however, took about 12-13 hours! So yeah, I'm pretty sure it's a problem with the hard drive.
After OS X was installed, the computer was faster than before but still slower than pre-Mavericks. Even though I just formatted everything, I decided to repair permissions on the drive and it repaired 4 errors. It didn't make the computer much faster though. I can however use the computer now, but it is still laggy and sometimes slow. Booting up the computer now only takes 1-2 minutes.
So what do you guys think? Is it definitely a hardware problem or is there something I haven't done that might fix it? As I said it's faster than before I reinstalled the OS X but I still won't be able to use a music production app, it is too slow for that.
I appreciate any answers!

Answer 1

 
1. Go to Finder> Click on "Go" from Menu Bar at the top of the Computer Screen> Select Computer from Drop Down Menu> Select Macintosh HD> Select /Library Folder> Select Caches Folder and Move it to Trash
2. Go back to "Go" in the Menu Bar at the Top of the Screen> Hold the Option Key on the Keyboard and select the Library Folder that appears under Home in the Drop Down Menu> Select Caches Folder and Drag to the Trash and select Merge
3. Go to Black Apple in the top left of the Computer Screen> Select System Prefrences from Drop Down Menu> Go To Users & Groups in fourth Row of Icons> Select Login Items at the top of the new Window> Clear out an unnecessary Programs by highlighting the Program and selecting the "-" at the bottom of the window next to the '+"
4. Go back to the Black Apple and then select Shutdown from the Drop Down menu
5. When Turning Computer Back on Boot into Safe Mode (Hold Shift Key after hearing the Startup Noise) Release Shift Key when you see Apple with Spinning Gear and Progress Bar underneath> Once at Login Screen Select shutdown Computer in Bottom Right of Screen
6. Now unplug any Preferral Devices (including Ethernet Cable, Keyboard, ext...) Take Plug out of the Back of the Computer this is known as reseting the SMC
7. Plug Everthing back in you unplugged, Turn on Computer, When you hear Startup Noise Hold Down all at the same time Command+Option+P+R, if you do this correctly the Screen should go Black, then White and make the Start up Noise Again, when you hear the Startup Noise for a Third Time, you can remove you hands from the Keyboard
8. Login like Normal
9. Continuation... If you have any Third Party Software such as Norton Anti Virus, MacKeeper (Malware), or any other types of Anti Virus software, Remove these from the Computer 
10. If those Troubleshooting Steps should fail, Verify and Repair Disk from Recovery HD,  Re Install OS from Recovery Partition as mentioned by Kappy, If you are running anything less than 6GBS of RAM, consider updating your RAM, if Re-Install does not Work, Make a back up of your Data, and then perform an Erase and Install