Any service shop should be able to identify the source of the problem in under 1/2 hour (labor). If they want more than that to identify the problem, go somewhere else.
Your problem could be any of the following:
AC adapter
DC powertap on laptop <<<<---- most likely!!!
Battery
Charging circuitry on motherboard
In a nutshell... check your AC adapter with a multimeter - if ok, then remove battery and see if laptop will work reliably w/ AC adapter (wiggle slightly to see if power dies or comes on). If power does not come on or power dies while wiggling power plug (slightly), then you probably have a bad DC powertap. If power stays on consistently during this test, you have narrowed it down to either a bad battery or failing DC-DC charging circuitry on the motherboard.
DC powertaps are easy to fix ($10-20 parts + 2-2.5 hours labor. (I fix them flat rate for $125).
Batterys and AC adapters can be mildly expensive ($75-120US)
Feel free to email me back if you have any more questions.
Best of success.