I recently upgraded and rebuilt my computer. New MB, CPU, RAM. I thought I had completed all BOINC work before I broke the old system down, but this project is claiming I have work units in flight that simply don't exist on my system.

Three questions:

Is there any way to abort those tasks through this website so that they can be re-issued?

Will the server give up after no trickle for a while?

Will those supposedly assigned tasks prevent me from getting new work units when they become available?

Thanks.

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Is there any way to abort those tasks through this website so that they can be re-issued?

Going to your account page and deleting the computer they were running on.

Will the server give up after no trickle for a while?

Yes but it is a long while!

Will those supposedly assigned tasks prevent me from getting new work units when they become available?

No, the, "two" computers under your account are treated separately.

Simpler still, just ignore them.

This project works on statistics; it's known that a lot of work never gets returned for various reasons, so lots more data sets than are needed are sent out.
And more still can be created if need be.

The server gives up after the artificial "deadline".

All failed tasks cause BOINC to slowly downsize the number that will be provided until it reaches one per day. Then successful tasks will increase it again to what ever value the project is using.

... I thought I had completed all BOINC work before I broke the old system down, but this project is claiming I have work units in flight that simply don't exist on my system. ...

... it could be the case that you did indeed complete all the work units on the old PC. When the CPDN server is very busy it sometimes issues 'phantom' models, which appear in your computer listings but which never arrive at the computer. For example, one of my computers claims to have five outstanding ANZ models - but they were never downloaded. They'll sit there until the deadline is reached (August 2015) and then be re-issued.

Ok, so you don't need to worry about them? I had an issue with my secondary hard drive and lost my BOINC data with 3 'long' tasks on it.