The JVC HR_DVSEK will play the Mini DV tapes, you then need to find a suitable output from the VCR.
I would suggest you use CVBS (known as video out), which would require you purchasing a SCART adapter such as the one here, which would plug into the SCART output on the VCR at one end, and into the computer at the other.
Next you would need a suitable video input adaptor for your PC, I would suggest something like the one here, as its USB so can be used on any PC\Laptop.
To record the mini DV onto your PC, you would run the software which comes with the video input adapter on the PC, set the SCART adaptor to output, and press play on your VCR at which point the video and audio content is then displayed on the PC at which point you can record it.
The total cost would be less than £10 and if ordered over the weekend should be with you by the end of the week.
Please let me know if you need anything clarified.