The charger port of my HTC sense is broken. how can I get it to work?

Isn't HTC Sense just the little add on bar on the bottom of most HTC's? Anyhow, this is usually unfixable by home made means, only a legit store can fix this if you have no warranty. I've tried on the Droid Incredible, Xperia Play, Sidekick 4g, HTC Evo, Galaxy Prevail, and Samsung Admire and only managed to "fix" one by pluging it in and wiggling the charger on it while attached as you mentioned. That was the Admire. The thing inside is just loose and luckily for you it still functions somewhat cause mine all died. You'll have to charge your battery on the other HTCs in order to avoid spending on a fix. BTW make sure its not the charger. And make sure there's no warranty by the company, remember theres a warranty you can buy which is when you buy the phone, and theres one that already comes with the phone usually for one year but you do need proof of purchase.