New Backup Admin seeking help

Well, you would look into running a differential backup. On the weekend it would run a full backup and the weekdays it would run only a backup of the files that have changed. But honestly, if you were recently put in charge of the backups. I would recommend a faster/larger tape drive. Don't try to make your current solution work when it's not getting a full backup every night. You're the one they'll be yelling at if something was lost because you tried to make due with what you have.

We are currently running a Differential backup every night with Full backups on the weekend. I talked them into getting me a new LTO3 drive, but now they want a full every night, we should be ok on size but I would still like to drop it down to make my backup window.

what program are you using to backup stuff?

If you're looking to cut down on size to meet the backup window, then I'd go through and uncheck ms office and other programs from the program files on the server. The stuff that you don't need to be backing up, it's just as easy to reinstall. Then uncheck your temp folders. Just go through and verify you need to be backing up those directories.

The problem with differential is when you have a system crash on Friday at 8pm and your full backup was scheduled for 9, you have to restore the last full backup, then all 4 tapes after that. Just very time consuming.

You may want to look at the cumulative incremental backup. All that would be required is the last full backup and the last cumulative incremental tapes. It has worked well for me in the past, and it shrinks the backup window on the weekdays.

We do not currently backing up anything on the C drives. ARCserve has a System State option that allows you to restore network settings and the like rather than backing all the settings up individually. I am looking at paring down files that have not been changed in over a year, but we have close to 400 Gig of data that I would need to sort through to find those files. I was hoping that someone may know of a program I could run that would allow me to specify a date and give me a list of folders that have not been modified since then. The end result would be that those would be backed up once and archived off as a Yearly or Quarterly backup so I do not have to waste time and space backing them up every week. If I can cut the backup size down enough I would run a full every night, eliminating the restore problems listed.

well, arcserve could do it pretty sure. a logging only job...or the Backup in
windows or hey, the log from your backup job...
so you can see, i don't quite fully understand your question but I will try to take it at face value: you can use free Robocopy from downloads.microsoft.com to report files modified. it is accompanied by a useful help file with examples.
test the backups

Well in ArcServe, I'm not sure how you could do this, but I know that in Yosemite Backup (www.yosemitetech.com) there are filters that you can set in the backup job, that let you define exactly what you are wanting.

For instance, if you do not want to backup files that have not been modified in the last year, there is a filter that can be defined for this. If you don't want to backup certain file types, there is a filter that can be defined for that. The users manual for this program has a very detailed section on filters.

ArcServe may have something like that too, I'm not sure (I don't particularly care for CA products myself).

If you are interested in persuing Yosemite Backup as a solution, there is a free trial with support available for 30 days. It is a simple solution and it meets your needs.