just to quickly clear up the possibility of network RAM: what is the make/model of your gateway? if you're running on a multi-part system, what are the makes/models of your routers/switches/modems?
otherwise, i doubt that's the issue anyway. here's what i need to know next:
obvious question, but have you updated your chipset or BIOS?
how many hard drives are installed? are you running on RAID (include the number) or IDE (SATA or AHCI)?
if you have multiple disks/partitions/drives, is your OS loaded separately from steam?
what are the read/write speeds of your drives?
what are the results of the SMART check pertaining to the health of your hard drives?
how much paging file size have you allocated (System, Advanced System Settings, Advanced, Performance -> Settings, Advanced, Virtual Memory)
what OS are you running?
do you have Windows Aero enabled? (disable it if so -- go into Control Panel, System, Advanced System Settings, Performance -> Settings, Visual Effects, and Adjust for best performance)
what is the security level of User Account Controls set to? (always beneficial to disable it when debugging a choke)
what programs start up with your computer? (if windows 7, go to start & search for msconfig, then go to the startup tab -- if windows 8, go to task manager & go to the startup tab)
immediately after booting (don't do anything besides the following), load steam & tf2, then dump the results of your task manager to a text file: http://www.intowindows.com/how-to-generate-text-file-list-of-running-processes-in-windows/
what is the rate convar set to on TF2?
upload the contents of your cfg folder so I can take a look.
what anti-viruses are you running?
disable any antiviruses, including Microsoft Security Essentials, for now
disable your firewall for now as well
make sure that cl_disablehtmlmotd is set to 1
some rudimentary ideas before i get the above info:
clean your demo folder for now
set rate to something much smaller for now, like 20000 (some servers will overload your NAT table -- if you have a small amount of RAM on your networking device -- if you don't throttle your rate)
unlock the true administrator account and try to run TF2 on it: http://teamfortress.tv/thread/15451/solved-mumble-overlay-doesnt-show
check fragmentation of your hard drives. defragment if there is any fragmentation, but also make sure that you're not automatically defragmenting your hard drives
run a DPC latency monitor in the background every time you play TF2, and stop it after the issue occurs: http://www.resplendence.com/latencymon
if your DPC spikes up to a level that the program alerts you about, then report the results & implement the advice in the following guide: http://www.overclock.net/t/1433882/gaming-and-mouse-response-bios-optimization-guide-for-modern-pc-hardware-2014-r0ach-edition (take the tone with a grain of salt -- ignore advice about disabling Hyper Threading and legacy options)
really unintuitive performance enhancements:
make sure that you've run the Windows Experience Index test
disable (and/or set to manual) any unnecessary services: http://www.blackviper.com/service-configurations/black-vipers-windows-7-service-pack-1-service-configurations/ (he has them for windows 8 as well)
ensure that windows is activated & that you've fully updated windows
if your TF2 is not loaded on an SSD with decent read/write speeds, here's a really shitty workaround for now until i can analyze your info:
offload TF2 to a RAMdisk and report the results