There are a few things that can cause this, since you're not getting the bulb/ballast error (blinking indicator lights) and the bulb is new... In order, these are the first things I would check... 1) verify that both fans are running adequately, I dont know the spec, they aren't super fast like a computer CPU, I believe around 200-500 RPM. 2) With an ohmmeter or continuity tester, check the lamp door switch: check that the switch closes as you move it, and stays closed as you toggle through it's range of motion. 3) Check/replace thermstat (detail below). 4) The switch board (buttons on side of the TV) is known to cause issues. See detail below. From here on out things get expensive...you'll want to buy or find a copy of the service manual, or if you're not technically oriented take it to a qualified repair shop, or disclose it's problem and unload it on craigslist for $100... 5) Check/replace main SMPS 6) Check/replace Ballast 7)Check/replace Main board 8)Check/replace DMD board.
(thermostat detail): The service manual I have for the 5676 shows a LED based lamp in the schematics (the 5676 is not a LED model, but uses a mercury discharge lamp)... therefore I can "educated guess" because connector CN805 where the thermstat plugs in serves a different function on the LED based models. The thermostat appears to be an electromechanical on/off switch. It should be closed (0 ohms) at room temperature. At some unknown temperature threshhold it should open/break continuity. Thermal switches of this nature fail often (also found in vehicle engines and furnace/AC). They either open prematurely at a lower temperature, dont open at all, or never close when appropriate. It's a $5 part if you've ruled out (1-2-4) above with no luck, I'd try replacing it before you graduate to costly board/ballast replacements.
(switch board detail): On the upper/right corner of the main board there is a group of 4 connectors. Switch board is the second connector from top corner (4 wires). Unplug that connector and try running the TV with the remote. There's a logic chip on the switch board that (my thereory is) gets zapped by static when you press a button or touch the chassis and thereafter malfunctions as if one or more buttons were intermitently or permanently depressed. The TV will still work with the remote when the switch board unplugged/disabled. Try it. I also have a HLT5075 intermittantly acted as though the volume down was depressed, the actual switches on the board tested fine (not physically stuck), unplugging the switch board from the main solved the issue. I could replace the board, but how often do I use those buttons... once a year?
Finally: Don't rule out the new bulb as a potential problem (even if it's a Phillips). I've picked up two of these 5676's in the last year off CL for $100 ea, the second one original owners sold because "it was dark, we replaced the bulb but it still wasnt half as bright as new..we decided to buy a new TV". They still had the recipt from the new bulb, a Phillips (verified - I looked at the markings on the reflector). I cleaned and probed assuming that new bulb was "good", replaced the ballast, worked on the SMPS, and wasn't getting anywhere. Eventually I took that new bulb to my sister's house and plugged it into the 5676 I gave her (that is nice and bright). Wholla! Failing/defective bulbs are well documented to produce dramatically more heat and trip the thermostat. Its not a problem with the thermostat (it's doing it's job preventing a fire hazard), it's the bulb. OE Phillips bulbs have a dramatically lower defect rate than aftermarket, but as I found, arent absolutely 100% either. My personal policy has become to buy aftermarket bulbs in pairs, run both of them through a burn in period (about 100 hours), then shelve one until it's needed. If you suspect one isn't right you'll have another to compare, and 100 hours will generally reveal critical defects within the warranty period. I personally have had great results with Buslink bulbs (between 3 TVs). One of them, a HLT5075 replaced OE with Buslink 2 years ago. That TV is on a minimum 8 hours/day the Buslink holding out well.
Edited by mrbrian200 - 2/20/13 at 1:23pm