I have a Compaq X1000/HPZT3000 (see X1000forums.com) and my A/C adaptor can get hot when both charging the battery and running the notebook at the same time so I try to avoid that or I make sure the A/C pack is in a well ventilated and unobstructed spot when using and charging the notebook.
If you have no excessive heat when using the battery and you can still charge the notebook with the cord with no overheating when the notebook is turned off this is similar to what I said above except your A/C adaptor has obviously gotten a kinked wire or some other issue that has caused it to go beyond just being hot (the A/C brick).
And I can assure you that my notebook never gets hot itself (Pentium M notebook) and I don't have a hot spot in any particular area.
So, definitely just get another A/C adaptor and you should be ok. If you could not charge the battery at all or had overheating when using the battery you could have a motherboard connection issue but you have not indicated that.
Note that there are two pieces to most HP/Compaq adaptors -- the plug to the wall can usually pull out of one side of the A/C adaptor to allow a foreign plug line to be used instead -- the part you are having trouble with is the A/C brick itself and the line going to the computer itself (not the wall) .. so save the A/C plug part if it will unplug.
You might be able to research Ebay for a cheaper pricing option on the A/C adaptor as opposed to hpshopping but of course you will get at least a 90 day hpshopping warranty on the part ordered through them I think .........
by the way, you may have your own user forum similar to mine (some are in the Compaq name as mine is) so either try ze5000forums.com or find out what the Compaq model equivalent is and try that --you may find user posts just like yours there (use Google to search for HP ze5000 posts in general) --your ze5385us is a prebuilt retail model version of the general ze5000 model -- find out the Compaq equivalent at hpshopping.com
I have an HP Pavilion ze5385us and recently I have noticed a problem with the place where the AC adapter plugs into the computer. I leave my laptop plugged in 99% of the time so I am not sure when this started, I only noticed it the last time I disconnected my laptop to use it in a different room. The plug was extremely hot (as was the corresponding corner of my laptop) when I went to grab it--it burned my fingertips. After I got it out of the notebook, I looked at the inside of the plug, which had a yellow circle inside of it before (I apologize for my lack of technical terminology!) but it now appears brown/black, sort of charred. Even after I let the computer and plug cool down completely, it heats up almost immediately again after being connected when I turn the computer on. I haven't noticed any difference in the functioning of my laptop yet, except for the fact that it will abruptly shut down once in awhile, but it has been doing that for at least a year, and it only occurs when the computer feels very hot (it mostly happens on very hot days in the summer, or if it's on my lap for a long period of time), but I never noticed the heat concentrated in one corner in those situations like it is now--it doesnt seem like those random shutdowns are connected to this problem. I unplugged and ran the notebook on battery power for an hour or so earlier today and it did not get excessively heated. After I had been running the laptop on battery for awhile, I shut it down, and then set it on my desk and plugged it into the AC adapter to charge it. After an hour or so of this, I went to feel the plug and the corresponding corner of my laptop, and they were not excessively heated. They were warm but not hot, and certainly nothing compared to the heat that burned my fingers. So, it appears that the excessive heating only occurs when it is plugged in while the laptop is on and in use. As of this time, the AC adapter is still able to power the computer and charge the battery, and the battery still functions normally by itself, however I know that charring cannot be good so I'm trying to avoid further disaster. I'm sorry if a lot of these details are unnecessary, but I don't have a lot of technical knowledge and wasn't sure what was or was not relevant.
I've had the laptop for 2 years and my warranty is expired so I was wondering if anyone here had any advice before I pay HP just to be able to speak to someone on the phone. I tried HP's online/email help and they said they suspected it could be the AC adapter (which even I could guess!) and suggested I plug a different AC adapter in to see if that works without overheating, but I don't have a second one, so that advice was kind of useless. I am just wondering if I should go ahead and order a new AC adapter from the HP website and hope that solves things, or whether I should bite the bullet and pay for a telephone consultation with HP, plus probably sending it in for them to evaluate and eventually buying the new AC adapter. If anyone has had this problem before or knows whether it is a problem wtih the AC adapter or something in the computer that is making the adapter heat up, I would greatly appreciate any advice. Thanks!

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