These games have had many updates over the past couple years, one of the big ones they did when they moved away from the social site was using the configuration in the installer folder. This is generally located here: C:\Program Files (x86)\Origin Games\Mass Effect 2\Binaries
MassEffect2Config. When you launch this you will do the following:
1. launch config program
2. click on Save Games
3. click copy Mass Effect Saved Games to the right
4. locate the ME save folder which is usually in C:\Users\user\Documents\BioWare\Mass Effect\Save
5. Once you copy that and save it, click the file tab and click save report.
When you launch the game, click on new game and click the import character. Now sometimes the game wont actually see that save file. In this case I would remove all folders from the save folder except the actual save you want to import.
I would also recommend disabling the cloud storage at this point as you might overwrite that save or sometimes it just wont see your save. What I personally would suggest is if this does not work, load the last save file for ME1, save as a new save file and then repeat the steps above.
Note: IF you do not see a ME save folder in any of your ME games, you can simply just create a "save" folder under the ME title under the documents folder. This is the default location that they save in. IF it doesnt show up it generally means that the folder is corrupted, or the saves are being sent to another location on the pc.