Consolidation of System and Boot partitions

I recently came upon a 160GB SATA hard drive from a cousin. It had Windows 7 32 bit installed on it and I wanted to install 64 bit Windows 7 on to it, but I accidentally did so in a new partition. The problem is that now the original 32 bit windows 7 is the System Partition, and the new one (which I use) is the Boot partition. I simply tried deleting the contents of the original partition, but this ended up requiring me to re-install windows on the partition I use. How would I go about marking the partition I use (which is C: New Folder in the picture I've posted for reference) as the system without breaking everything or having to move everything over to the old one (F: 1) and re-reinstall Windows 7 64 bit there??

https://i.imgur.com/lJuXQeF.png

The software you recommended would have been ideal if I needed to move the boot, but it's the system that needs to be moved. Furthermore for some reason, trying to access Computer Management isn't working.

So, would I be able to delete the contents of the system partition and integrate it into the empty space into the boot partition with no ill effects?

What you want is to move the System (boot files) to C, which is done by marking C Active and then running Startup Repair - Run up to 3 Separate Times to write the boot files to C, run many tests to confirm it's bootable, write the Repair link to F8 Boot tools menu. EasyBCD does not do all of this.

Once the System Active flags are on C (Boot only means its the currently-booted partition) you can delete F after copying off any files you need, then recover its space into C if you want using Partition Wizard CD to Resize Partition - Video Help.

However if you have bugs with Win7 Disk Mgmt not working then I'd consider following the steps closely to get a perfect Clean Reinstall - Factory OEM Windows 7 especially deleting all partitions during install.