I don't of any apps that would do it, as far as I know you should always get the icon in the notification bar that the phone is connected to a computer/usb debugging is on. Factory reset is always an option, or uninstall every app you've installed since right before it stopped working.
The port can definitely be partially broken (pins misaligned).
*sigh* - I was afraid it would come to this. Thanks anyway, but with my setup it's not something worth the pain of another reset, so long as I can charge my battery, and can still transfer to SD through another device. At least my screen still works. I just wanted to be sure that my phone couldn't be fixed more easily, and then it's important to raise awareness of such aggravations for those who would consider buying HTC products.
There is quite a lot to like about DINC, no doubt, but solidity of construction is a critical factor. I have twice developed a problem when my screen would chronically die at random (not the time span in my settings, and often after only two seconds). Reset and reinstallation did nothing for this, and the end result was replacement of my phone. I was rather shocked at how quickly Verizon came to the decision for this, as if they were aware of something which they would rather avoid discussing, therefore quick appeasement would be their policy.
Another thing which I read somewhere were some statements made by those claiming to have been involved with Verizon that all returns are replaced by other returns, which are "refurbished". I would do some homework to provide verification on such a claim if it wasn't so necessarily believable. How else would they replace your DINC with the same product which you bought, when you return it a year after the last of that model has been sold? What they should do is replace it with the current generation of that product, or something similar (such as the DINC with SLCD screen, which would be much better for navigation in bright sun than the AMOLED model), but I know for a fact that they don't do this.
Somewhere I read that a heavy percentage of DINC phones had processor chip sets which were imperfectly soldered, which would lead to eventual shorting and degradation of the device. Perhaps this is an issue which is prevalent throughout the industry, wherever the labor is cheap, and in abusive sweatshop conditions? If so, it may be a problem with any such device, no matter who owns it, but no less where company ownership happens to be schooled in the same competitive values system which fueled world controversy at the Beijing Olympics.
Have I made clear enough why some problems are as likely caused by the device production as the apps which I choose? Please forgive if I come off as rather brash, being new to posting here, but I have been through enough to know, with wasted hours adding up not to days but weeks out of my life. I would put a lot of money down on a bet that removing every app which I have installed still won't fix my connectivity problem.