What can I do about frequent beach ball Safari and other apps?
Once I got something similar after a Snow Leopard upgrade:  spinning bechball when starting Safari and making Safari inoperable. Turned out it was an incomaptible SIMBL plugin from before the OS upgrade.

If you already replaced the motherboard and hard drive, there's really not much "hardware" left that can be eliminated.

If you already have done a clean install as well, there is really no other "software" eliminated either. Make sure you've done a total clean install though: format HDD, install the base OS without iLife, etc, DO NOT restore anything from you backup afterwards, DO NOT use your regular username and DO NOT enter your Apple ID at first boot. Do not restore and data from your backup, especially not /Library and /Users//Library

I guess I'd also try to install a different version of OSX (downgrade or upgrade, doesn't matter) and see if the problem persists.  Also try booting a different OS (Windows, Linux, boot from a Linux live CD/usb would be the easiest option). Booting in a different OS is the best way to find out if it's a hardware issue or software.

Generally a spinning beachball are caused by CPU/memory/disk access spikes, but it can also be some other kind of blocking I/O (e.g. network, USB). Maybe it's compatibility issues with your home network? Use it on a different network, try connecting to the network with an external USB ethernet adapter.

Hope that helps.