Boot up waaaay too slow

I have a Toshiba note c55 a5310( Win 8.1 pro w/ updates as of Jan., i3, 6gb ram, hdd) awhile ago I installed a video editing prog (can't remember name now) and inadvertently deleted some files I shouldn't have from registry when I deleted program. Boot problems began and I did all kinds of digging: sfc/scannow, chdsk, startup app and driver to no avail. I just did a clean install- deleted all partitions (not with DBAN though), UEFI install and still get this very long hang ~4 min when I boot. I changed things back in BIOS- boot sequence HDD first, re-enabled secure boot and fast boot enabled. System runs fine otherwise it's just the boot time is way too slow and I don't understand especially in light of the new install. Any suggestions would be greatly appreciated.

Some of the MS updates cause the defragger to slow my laptop down. The slowdown occurs as the disk becomes fragmented as old files are deleted, and new files are added.

Watching task manager and resource monitor illuminated this for me. After an update, letting the laptop run for a while resolves the issue.

A clean install from older disks causes a backlog of updates, and leaves the computer more vulnerable until all the security updates complete.

Have you checked for the presence of unwanted startup programs? CCleaner has a Tab called Startup in Tools that you can edit easily.

You can try this command line HDD defrag batch file I made for someone else with a slow system. It invokes windows boot optimization that usually happens every once in a while (3-5 boots I think) and it consolidates the free space so that the free space isn't so fragmented and programs have room to install/grow without fragmentation. Just unzip>drag the shortcut to desktop if you wish>it has to run with Admin privileges so the shortcut ask for them. A command prompt window will open and run each phase one after another...it can take some time so go take a bath, watch tv, or eat dinner. There are instructions included to expand it to other disk if you want.
Laptop have slow(5400rpm) disks anyhow, so its important to defrag after any major installs/uninstalls/large file moving.

There is a way to optimize your computer without installing anything; some items in this tutorial can help startup times: http://www.eightforums.com/tutorials/37511-optimize-performance-windows-8-a.html I warn though, that I never recommend using optimizers (programs to 'speed up windows'), registry cleaners (Ccleaner is good if you know what you're doing), or 3rd party defragmenters.

Update the BIOS, drivers, etc.

If your laptop allows you to, and if all software options fail, replace the hard drive with an SSD. SSDs have a much faster boot up time and can help quite a bit with these issues.

Try upgrading ram.
How much do you have currently?