If the following suggestions work, please let me know and you can Accept the answer (and if possible, leave positive feedback). If not, please DO NOT Accept the answer. Instead, let me know and we'll try some more things or I can refer you to another Expert who may be able to help you further.
If you get me the details on the machine, we can find out if you have room for more RAM. That would help, especially for a program like FCP. I would need you to look up the serial number on the site below and then post the pertinent info here (prod year, model identifier, processor speed, etc). The serial number can be found in the apple menu / about this mac / more info.http://www.powerbookmedic.com/identify-mac-serial.php
Next, I'd suggest Firefox for your browser (you said you use Safari). This won't keep the machine from locking up necessarily, but in my opinion, Firefox is a faster, smoother browser and it also autoupdates when new versions are available.http://www.mozilla.com/en-US/firefox/personal.html
Before we go any further, I would suggest you use a program like Carbon Copy Cloner (http://www.bombich.com/
) to create a restorable backup of your Hard Drive to an External Hard Drive. This free program will make a mirrored copy of your hard drive in it's current state that you can go back to if things go south or if the PowerMac does take an unrecoverable crap. I do this personally before I perform any kind of install, update or major change to my system. In fact, I do it religiously to all of my office machines on a weekly basis. It has saved me countless hours of headaches and time.
Last, I would suggest you run some general maintenance on the computer. It is an obvious square-one approach. I normally suggest this first because it is good practice plus if we dig too deep into a problem and simple measures could have repaired it in the beginning we'll be kicking ourselves later... This is going to be a long email so I suggest printing it out for your reference.
First let's reset the PRAM on the computer.
1) Shut down the computer.
2) While the computer is shut down, locate these keys: command (has an apple on it), option (sometimes called alt), P, and R.
3) Turn the computer on, then press and hold Command-Option-P-R before the gray screen appears.
4) Hold these keys down until you hear the startup sound a total of 3 times.
5) Release the keys.
Next, let's try a Safe Boot. This will perform several clean up procedures that may be affecting the machine's performance and startup.
1) Shut down your computer completely.
2) Start up the computer and immediately after the startup chime, press and hold the Shift key
3) Once the gray Apple and progress indicator appear, release the Shift key
4) Note: Startup will likely take substantially longer than normal
5) In Mac OS 10.4 or later, you will have to login to your account, even if it normally does so automatically.
6) Shut down the computer.
Now let's check / repair the disk permissions. Although this doesn't fix all problems it is a great way to start when working on a machine, besides it often cleans up any other smaller problems you may or may not be experiencing.
1) Restart the machine.
2) Before you have opened any programs, go to Applications / Utilities / Disk Utilities.
3) Run the Verify Permissions, then Repair any errors it finds.
4) Shut down the computer.
Last, let's run an fsck in Single User Mode:
1) Start the mac and hold down the apple key (Command) and the S.
2) After the Apple logo (and if the hard drive can mount), it will have a black screen with white text. When it finally stops loading and you are given a prompt, type this command EXACTLY (there is only a space between "k" and "-") and then press return:/sbin/fsck -fy
fsck will go through five "phases" and then display info about your hard disk's state. Once it finishes, it'll display this message if no issue were found:** The volume (name_of_volume) appears to be OK
If fsck found issues and has done anything, it will display this message:***** FILE SYSTEM WAS MODIFIED *****
If the above message appears, repeat the fsck command until fsck tells you that your volume "appears to be OK"
The first-pass repairs may uncover additional issues, so it's normal to have to do it more than once.
3) When fsck reports that your volume is OK, type the following EXACTLY and press return:reboot
Hopefully you'll be able to see a noticable difference in performance on the machine after this. As long as you take necessary steps (Carbon Copy Cloner), I wouldn't be afraid to use the machine. In fact I have a 20+ Apple IIGS that still runs here at the house. It doesn't do much, but it's one helluva conversation piece.
Enjoy! and Good Luck!