The original default was either 15000 or 20000 & I increased it a few times over the years. Increasing it tenfold might cause problems. Best idea would be to save the report into a text file & upload that as an attachment.

Thanks. OK, here they go as Console save as.

For WireShare:
JavaApplicationStub_2014-08-25-010524_MacOSX-G.wakeups_resource.spin

For LimeWire
org.limewire.ui.swing.Main_2014-08-24-181454_MacOSX-G.wakeups_resource.spin

As far as I understand, ".spin" is a text file. If you cannot open it, just let me know and I will upload it as ".txt".

When I tried to upload to the forum, I got:
Your file of 206.3 KB bytes exceeds the forum's limit of 200.0 KB for this filetype. So, I have compressed them both as ConsoleFiles.zip (47.3 KB)

I just downloaded the LPE 5.6.2 "Package" and installed the Windows version on a Win 7 system. It appears to install without problem, but when launched, tells me I need Java 6.0 or above. I verified my Java Enviroment and have 7.0, both 64 and 32 bit versions installed. (I use different browsers) Every time I launch, it gives the "Need Java" message and take me to the Oracle site. Even after a shut down and restart. Any suggestions?

If you prefer to use LPE, you need to install LimeStart & launch LPE via LimeStart (LimeStart is included in the package.) Installing LimeStart will replace all of the original LPE shortcuts & point to LimeStart instead. Alternatively if you install WireShare then the problem is fixed without need for LimeStart. WireShare has also fixed several other bugs in regards to Java 7. WireShare should also arguably be a little easier to connect with. WireShare (released this year) uses the same sourcecode as LPE (released 2010), bug fixes and improvements have been made & should run more smoothly than LPE.
If you decide to install WireShare, then you should probably first uninstall LPE. Though both can coexist on the system.

Thanks for the files. Console has no problem opening them. Normally I'd have thought 200 KB would be more than sufficient for a standard text file. But yours are considerably large. :D (I think the original forum default for text files was only about 20 KB.)

I have finally done the tests with a brand newly created account, as well as booting from a different disk.

When I create a new account and run WireShare 5.6.4.1, the same previously reported issues remain (pesky window indicating "WireShare has encountered an internal error" and no connection).

When I boot from a different disk (pendrive in which nothing except the Mac OS X 10.9.4 Mavericks was installed), I installed the latest Oracle Java 7 (1.7.0_67) and WireShare and all worked fine (no pesky window and turbo-charged connection in less than one minute). Both for 32- and 64-bit mode.

If then I install Java 6 (1.6.0_65) on such pendrive, the pesky window does not show, but I get no connection. For both 32- and 64-bit mode WireShare always shows Java 6.

When I uninstall Java from such pendrive and re-install Java 7, all works again.

Update: I have uninstalled Java from the Mac mini and re-installed Java 7 only, but the same issues remain (pesky window and no connection).

Amazing test results. :) So glad to hear about the success using an alternate start-up drive.

MacOSX's Java 6 can be difficult to totally uninstall. If there are any other apps or utilities that utilize it or perhaps have indirect unix links to it.

When I earlier hinted at removing Java cache /& settings files, I'm now wondering if this might actually be worthy to try. There's something on your system related to java that's obviously an issue.

And perhaps Java 7 is the go for you. But you now know how to force WS to use it.

Wow, wow, wow!!!

I finally could make ShareWire to work in the Mac mini (turbo-charged connected to five hosts)!!!

I just replaced the following items of the Mac mini using the ones of the pendrive in which WireShare worked:

/Library/Java

/System/Library/Frameworks/JavaFrameEmbedding.framework
/System/Library/Frameworks/JavaScriptCore.framework
/System/Library/Frameworks/JavaVM.framework

/System/Library/Java

And then re-installed WireShare, which is NOT set as 32-bit mode by default (File - Get Info; it did not connect if 32-bit mode was selected, which is the installation default!!!). In any case, since Java 6 is not present, it always showed Java 1.7.0_67.

On the other hand, as previously indicated, WireShare - Preferences - Advanced
is set as default:
Gnutella port - Use Universal Plug 'n' Play (Recommended)

BitTorrent ports - Use Universal Plug 'n' Play (Recommended)

I think that replacing the
/Library/Java
was the one that did the trick, because previously I had replaced the other ones to no avail. Setting it NOT to 32-bit mode could have also fixed it.

So, problem solved. Here I leave it for future reference, in case it may help someone.

Many thanks to all and specially to Lord of the Rings for all the kind support.

BTW, I have found that the files cannot be added to My Files (library or public shared) if they end in .sit, .dmg, etc., which should be a flaw or bug, since many files in Mac have such extension. Curiously, it is possible to add such very same files if they end in .sitx, .dmgx, etc.

On the other hand, with Gnutella port - Use Universal Plug 'n' Play (Recommended), sometimes WireShare connects as turbo-charged to five servers in just one minute, but other times it takes more and even much more (for instance, a whopping 26 minutes). Is there a way to improve that?