It could be a plethora of things.
I'm going to do a series of question, and info sort of thing pfcjma.
1) When disassembling the laptop;
A) Did you work on table?
B) Used an ESD wrist strap, and connected the alligator clip to a good ground source?
Or alternatively found a proper way to relieve your body of Static electricity?
Fling the motherboard in the trash.
2) When the shop soldered the DC Power Jack, was the Processor, and Ram Memory removed? Everything removed down to the bare motherboard?
Prepare to replace the Processor, and Ram Memory if installed.
(Don't forget to Properly clean the top of the Processor's case, and the bottom of the metal pad on the Fan/Heatsink Assembly, and apply fresh, new Thermal Paste)
3) Did the shop perform a good solder connection, and not a cold solder joint/s, or burn the circuit traces where the jack solders into?
Prepare to have the solder joints re-soldered by a competent tech.
If the circuit traces are burnt, and will not accept a tinning, toss the motherboard.http://www.powerjackrepair.org/toshibasatellitem35x-s161.html
(No, not my shop, nor am I advertising for them. Just showing you a competent soldering job on the DC Power Jack, for a Toshiba Satellite M35X-S161)
4) Is the replacement DC Power Jack THE correct one, or off of someplace like Ebay?
Not the correct one, and some of the pins didn't line up with the holes in the circuit traces, where a rinky-dink job had to be performed to install the jack?
The answer is obvious.
4) There are fuses on the motherboard. Were these checked?
From the Service Manual;
Power Supply Troubleshooting
> Check Power Supply Status (Procedure 1)
>Are the DC IN and Battery LED's lit?
Replace adapter/battery (Procedure 2)
Check Power Supply connections (Procedure 3)
> Can you turn the computer on?
Are the internal power connections secure?
Perform internal connection check (Procedure 5)
Replace the motherboard
The system board may be disconnected or damaged. Disassemble the computer following the steps described in Chapter 4, Replacement Procedures. Check the connection between the AC adapter and the system board. After checking the connection, perform Check 1:
Check 1 Use a multi-meter to make sure that the fuses on the system board are not blown. If a fuse is not blown, go to Check 2. If a fuse is blown, go to Check 3.
You are checking to make sure there is continuity, from the center pin of the DC Power Jack to the motherboard.
You are also checking to make sure there is continuity from the outside shell, ( that is around the center pin), of the DC Power Jack to the motherboard.
OHM's test with a multimeter.
An economical multimeter is around $5 to $12.
If no continuity is found, check the fuses }
Check 2 Make sure that the battery cable is firmly connected to the system board. If it is connected firmly, go to Check 3.
Check 3 The system board may be damaged. Replace it with a new one following the instructions in Chapter 4.
Just wanted to note that there are fuses on the motherboard.
Here is the download page for the free Service Manual,http://www.tim.id.au/blog/tims-laptop-service-manuals/#toc-toshiba
On this page go down to line 11.
The one that starts with Satellite A10.
In this paragraph of file names go to the 3rd line down.
Go across and click on M30X.
The M30X and M35X are the same in regards to disassembly, and troubleshooting procedures.
This is a PDF file. Allow a few seconds for the first page to come up, after you click on the above link, and additional time for the file to fully download.
Troubleshooting Procedures - Page 31
Troubleshooting Flowchart - Page 37
Power Supply Troubleshooting - Page 41
Have questions post in a Comment.